Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
65470 conjugacy classes of subgroups; only the 32651 normal subgroups are shown.
This group has 65470 conjugacy classes of subgroups — too many to draw. Only its 32651 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C25 | C22×D7 |
| commutator, cosocle | C2×C7 | C27 |
| Frattini | C2 | C26×D7 |
| Fitting | C24×C7×D4 | C2 |
| socle | C25×C7 | C23 |
| hypercenter | C24×D4 | D7 |
| hypocenter | C7 | C24×#41 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C25 ◁ C24×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×C7×D4 | C2 | semidirect |
| 2. C24×C22⋊D7 | C2 | semidirect |
| 3. C25×Dic7 | C2 | semidirect |
| 4. C23×#1159 | C2 | direct (N × H) |
| 5. C24×C4×D7 | C2 | semidirect |
| 6. C24×Dic14 | C2 | semidirect |
| 9. C23×C7×D4 | C22 | semidirect |
| 11. C23×C22⋊D7 | C22 | semidirect |
| 14. C24×Dic7 | C22 | semidirect |
| 15. C22×#1159 | C22 | direct (N × H) |
| 16. C23×C4×D7 | C22 | semidirect |
| 17. C23×Dic14 | C22 | semidirect |
| 24. C22×C7×D4 | C23 | semidirect |
| 26. C22×C22⋊D7 | C23 | semidirect |
| 29. C23×Dic7 | C23 | semidirect |
| 30. C2×#1159 | C23 | direct (N × H) |
| 31. C22×C4×D7 | C23 | semidirect |
| 32. C22×Dic14 | C23 | semidirect |
| 36. C24×D4 | D7 | semidirect |
| 40. C24×C7 | #41 | semidirect |
| 45. C2×C7×D4 | C24 | semidirect |
| 47. C2×C22⋊D7 | C24 | semidirect |
| 50. C22×Dic7 | C24 | semidirect |
| 51. #1159 | C24 | direct (N × H) |
| 52. C2×C4×D7 | C24 | semidirect |
| 53. C2×Dic14 | C24 | semidirect |
| 59. C23×D4 | C2×D7 | semidirect |
| 66. C23×C7 | C2×#41 | semidirect |
| 71. C7×D4 | C25 | semidirect |
| 73. C22⋊D7 | C25 | semidirect |
| 76. C2×Dic7 | C25 | semidirect |
| 77. C4×D7 | C25 | semidirect |
| 78. Dic14 | C25 | semidirect |
| 87. C22×D4 | C22×D7 | semidirect |
| 94. C22×C7 | C22×#41 | semidirect |
| 105. C24 | #1159 | direct (N × H) |
| 111. C2×D4 | C23×D7 | semidirect |
| 118. C2×C7 | C23×#41 | semidirect |
| 124. C23 | C2×#1159 | direct (N × H) |
| 129. D4 | C24×D7 | semidirect |
| 135. C7 | C24×#41 | semidirect |
| 139. C22 | C22×#1159 | direct (N × H) |
| 147. C2 | C23×#1159 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C7×D4 | 2 |
| C24×C22⋊D7 | 2 |
| C25×Dic7 | 2 |
| C23×#1159 | 2 |
| C24×C4×D7 | 2 |
| C24×Dic14 | 2 |
| C24×#41 | 7 |