Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D73 |
| commutator | C4×C73 | C23×C4 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #419×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #419 | D73 |
| hypocenter | C73 | #2949 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #419 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17989065 | C2 | semidirect |
| 4. #17988690 | C2 | semidirect |
| 5. #17988672 | C2 | semidirect |
| 6. #17988623 | C2 | semidirect |
| 8. #17988545 | C2 | semidirect |
| 9. #419×C73 | C2 | semidirect |
| 11. C2×#11924015 | C4 | semidirect |
| 16. Q8×Dic73 | C22 | semidirect |
| 23. #14556524 | C22 | semidirect |
| 24. #14556522 | C22 | semidirect |
| 26. #14556501 | C22 | semidirect |
| 27. C8×Dic73 | C22 | semidirect |
| 31. #103×C73 | C22 | semidirect |
| 38. #11924015 | C2×C4 | semidirect |
| 39. #11924015 | C2×C4 | semidirect |
| 40. C2×#10596831 | C2×C4 | semidirect |
| 54. C2×Q8×C73 | C2×C4 | semidirect |
| 104. C73 | #2949 | semidirect |
| 111. #419 | D73 | semidirect |
| 132. #103 | C2×D73 | semidirect |
| 139. C2×Q8 | C4×D73 | semidirect |