Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2080 conjugacy classes of subgroups; only the 302 normal subgroups are shown.
This group has 2080 conjugacy classes of subgroups — too many to draw. Only its 302 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C22×C7×#41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C7×#535 | C2 | semidirect |
| 2. C2×C7×#447 | C2 | semidirect |
| 3. C7×#1999 | C2 | semidirect |
| 4. C7×#1875 | C2 | semidirect |
| 5. C7×#1780 | C2 | semidirect |
| 7. C23×C7×D4 | C22 | semidirect |
| 13. C2×C7×#121 | C22 | semidirect |
| 16. C2×C7×#117 | C22 | semidirect |
| 18. C2×C7×#102 | C22 | semidirect |
| 19. C2×C7×C22⋊C8 | C22 | semidirect |
| 20. C2×C7×C22⋊C8 | C22 | semidirect |
| 21. C7×#340 | C22 | semidirect |
| 22. #23925 | C7 | direct (N × H) |
| 46. C7×#121 | D4 | semidirect |
| 58. C2×#535 | C2×C7 | semidirect |
| 59. C2×#447 | C2×C7 | semidirect |
| 60. #1999 | C2×C7 | semidirect |
| 61. #1875 | C2×C7 | semidirect |
| 62. #1780 | C2×C7 | semidirect |
| 109. C23×D4 | C22×C7 | semidirect |
| 115. C2×#121 | C22×C7 | semidirect |
| 118. C2×#117 | C22×C7 | semidirect |
| 120. C2×#102 | C22×C7 | semidirect |
| 121. C2×C22⋊C8 | C22×C7 | semidirect |
| 122. C2×C22⋊C8 | C22×C7 | semidirect |
| 123. #340 | C22×C7 | semidirect |
| 184. #121 | C7×D4 | semidirect |
| 304. C7 | #23925 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#535 | 2 |
| C2×C7×#447 | 2 |
| C7×#1999 | 2 |
| C7×#1875 | 2 |
| C7×#1780 | 2 |
| #23925 | 7 |