Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
528 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 149 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 | C23×D73 |
| commutator, socle | C23×C73 | C24 |
| Fitting | #391×C73 | C2 |
| hypercenter | #391 | D73 |
| hypocenter | C73 | #2732 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556567 | C2 | semidirect |
| 2. #17988524 | C2 | semidirect |
| 3. #17988519 | C2 | semidirect |
| 4. #17988509 | C2 | semidirect |
| 6. #17988485 | C2 | semidirect |
| 8. #17988461 | C2 | semidirect |
| 9. #391×C73 | C2 | semidirect |
| 35. C2×D292 | Q8 | semidirect |
| 56. C2×Q8×C73 | D4 | semidirect |
| 130. C73 | #2732 | semidirect |
| 135. #391 | D73 | semidirect |
| 165. C2×Q8 | D292 | semidirect |