Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2070 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 2070 conjugacy classes of subgroups — too many to draw. Only its 501 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×#2840 | C2 |
| hypercenter | #2840 | D7 |
| hypocenter | C7 | #36675 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#2840 | C2 | semidirect |
| 2. #11734331 | C2 | semidirect |
| 3. #11734304 | C2 | semidirect |
| 4. #11734224 | C2 | semidirect |
| 5. #11734222 | C2 | semidirect |
| 6. #11731305 | C2 | semidirect |
| 7. #11731263 | C2 | semidirect |
| 9. C22×#1161 | C22 | semidirect |
| 11. C2×Q8×Dic7 | C22 | semidirect |
| 16. #90003 | C22 | semidirect |
| 17. #90001 | C22 | semidirect |
| 24. #89446 | C22 | semidirect |
| 25. #89444 | C22 | semidirect |
| 26. #89438 | C22 | semidirect |
| 27. #89432 | C22 | semidirect |
| 28. #89420 | C22 | semidirect |
| 56. #2840 | D7 | semidirect |
| 65. C24×C7 | #41 | semidirect |
| 183. C24 | #1161 | semidirect |
| 240. C7 | #36675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2840 | 2 |
| #11734331 | 2 |
| #11734304 | 2 |
| #11734224 | 2 |
| #11734222 | 2 |
| #11731305 | 2 |
| #11731263 | 2 |
| #36675 | 7 |