Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
8094 conjugacy classes of subgroups; only the 1123 normal subgroups are shown.
This group has 8094 conjugacy classes of subgroups — too many to draw. Only its 1123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D7 |
| commutator, socle, cosocle | C23×C7 | C25 |
| Fitting | C7×#2867 | C2 |
| hypercenter | #2867 | D7 |
| hypocenter | C7 | C2×#2867 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #2867 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D7×#127 | C2 | semidirect |
| 2. C7×#2867 | C2 | semidirect |
| 3. #11740630 | C2 | semidirect |
| 4. #11730763 | C2 | semidirect |
| 5. C43×D7 | C2 | semidirect |
| 7. C2×C7×#127 | C22 | semidirect |
| 8. C2×#6503 | C22 | semidirect |
| 10. C2×#6437 | C22 | semidirect |
| 12. C43×C7 | C22 | semidirect |
| 13. C42×Dic7 | C22 | semidirect |
| 26. C42×D7 | D4 | semidirect |
| 30. #2867 | D7 | direct (N × H) |
| 43. C42×C7 | C2×D4 | semidirect |
| 44. C4×Dic7 | C2×D4 | semidirect |
| 49. C2×#127 | C2×D7 | semidirect |
| 52. C43 | C2×D7 | semidirect |
| 63. C4×D7 | #127 | semidirect |
| 81. C4×C7 | C2×#127 | semidirect |
| 82. Dic7 | C2×#127 | semidirect |
| 95. C42 | D4×D7 | semidirect |
| 99. D7 | #2867 | direct (N × H) |
| 111. C7 | C2×#2867 | semidirect |
| 118. C4 | D7×#127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×#127 | 2 |
| C7×#2867 | 2 |
| #11740630 | 2 |
| #11730763 | 2 |
| C43×D7 | 2 |
| C2×#2867 | 7 |