Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D292 |
| commutator | C2×C4×C73 | C24 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #408×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #408 | D73 |
| hypocenter | C73 | #3200 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C2×#41 ◁ #408 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989158 | C2 | semidirect |
| 3. #17988929 | C2 | semidirect |
| 4. #17988912 | C2 | semidirect |
| 5. #17988833 | C2 | semidirect |
| 6. #17988816 | C2 | semidirect |
| 7. #17988740 | C2 | semidirect |
| 8. #17988728 | C2 | semidirect |
| 9. #408×C73 | C2 | semidirect |
| 10. C22×Dic146 | C22 | semidirect |
| 21. #14556570 | C22 | semidirect |
| 27. #14556550 | C22 | semidirect |
| 28. #14556525 | C22 | semidirect |
| 29. #14556523 | C22 | semidirect |
| 30. #14556516 | C22 | semidirect |
| 31. #14556516 | C22 | semidirect |
| 35. C2×M16×C73 | C22 | semidirect |
| 36. C22×C8×C73 | C22 | semidirect |
| 38. C22⋊C8×C73 | C22 | semidirect |
| 138. C73 | #3200 | semidirect |
| 147. #408 | D73 | semidirect |
| 153. C2×M16 | C2×D73 | semidirect |
| 154. C22×C8 | C2×D73 | semidirect |
| 176. C22⋊C8 | C2×D73 | semidirect |