Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
4086 conjugacy classes of subgroups; only the 811 normal subgroups are shown.
This group has 4086 conjugacy classes of subgroups — too many to draw. Only its 811 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×#2868 | C2 |
| hypercenter | #2868 | D7 |
| hypocenter | C7 | #36644 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #2868 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#90416 | C2 | semidirect |
| 2. C7×#2868 | C2 | semidirect |
| 3. #11740696 | C2 | semidirect |
| 4. #11731820 | C2 | semidirect |
| 5. #11731764 | C2 | semidirect |
| 6. #11730763 | C2 | semidirect |
| 7. C43×D7 | C2 | semidirect |
| 46. C42×D7 | D4 | semidirect |
| 48. #2868 | D7 | semidirect |
| 73. C42×C7 | #41 | semidirect |
| 111. C4×D7 | #127 | semidirect |
| 143. C4×C7 | #532 | semidirect |
| 169. C42 | #1161 | semidirect |
| 193. C7 | #36644 | semidirect |
| 204. C4 | #90416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90416 | 2 |
| C7×#2868 | 2 |
| #11740696 | 2 |
| #11731820 | 2 |
| #11731764 | 2 |
| #11730763 | 2 |
| C43×D7 | 2 |
| #36644 | 7 |