Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
932 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 153 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 | #392×C73 | C2 |
| hypercenter | #392 | D73 |
| hypocenter | C73 | #2615 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11924027 | C2 | semidirect |
| 2. C2×#14556564 | C2 | semidirect |
| 3. C2×#14556563 | C2 | semidirect |
| 4. #17988500 | C2 | semidirect |
| 5. #17988499 | C2 | semidirect |
| 6. #17988496 | C2 | semidirect |
| 7. #17988495 | C2 | semidirect |
| 8. #17988495 | C2 | semidirect |
| 9. #17988446 | C2 | semidirect |
| 10. #17988445 | C2 | semidirect |
| 11. #392×C73 | C2 | semidirect |
| 58. C22×Dic73 | D4 | semidirect |
| 64. C2×C4×D73 | D4 | semidirect |
| 178. C73 | #2615 | semidirect |
| 187. #392 | D73 | semidirect |