Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
176 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14556563 |
| commutator | C42×C73 | C23 |
| Frattini | C42 | C22×D73 |
| Fitting | #461×C73 | C2 |
| socle | C22×C73 | #121 |
| hypercenter | #461 | D73 |
| hypocenter | C73 | #1701 |
| LCS | G ▷ C42×C73 ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #461 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17988935 | C2 | semidirect |
| 3. #17988665 | C2 | semidirect |
| 4. #17988337 | C2 | semidirect |
| 5. #17988333 | C2 | semidirect |
| 6. #17988330 | C2 | semidirect |
| 7. #461×C73 | C2 | semidirect |
| 85. C73 | #1701 | semidirect |
| 87. #461 | D73 | semidirect |