Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
604 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 141 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 | #383×C73 | C2 |
| hypercenter | #383 | D73 |
| hypocenter | C73 | #2598 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×D292 | C2 | semidirect |
| 2. C2×#14556548 | C2 | semidirect |
| 3. #17988527 | C2 | semidirect |
| 4. #17988524 | C2 | semidirect |
| 5. #17988505 | C2 | semidirect |
| 7. #17988479 | C2 | semidirect |
| 8. #17988465 | C2 | semidirect |
| 9. #17988465 | C2 | semidirect |
| 10. #17988461 | C2 | semidirect |
| 11. #383×C73 | C2 | semidirect |
| 71. C42×C73 | D4 | semidirect |
| 146. C73 | #2598 | semidirect |
| 157. #383 | D73 | semidirect |
| 217. C42 | D292 | semidirect |