Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C4×C73 | C23×C4 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #405×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #405 | D73 |
| hypocenter | C73 | #2949 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17989064 | C2 | semidirect |
| 4. #17988689 | C2 | semidirect |
| 5. C4×#11924017 | C2 | semidirect |
| 6. #17988625 | C2 | semidirect |
| 7. #17988597 | C2 | semidirect |
| 9. #405×C73 | C2 | semidirect |
| 12. C2×#11924017 | C4 | semidirect |
| 15. C4×Dic146 | C22 | semidirect |
| 23. #14556525 | C22 | semidirect |
| 24. #14556523 | C22 | semidirect |
| 25. #14556516 | C22 | semidirect |
| 30. #97×C73 | C22 | semidirect |
| 31. C4×C8×C73 | C22 | semidirect |
| 35. C2×Dic146 | C2×C4 | semidirect |
| 43. #11924017 | C2×C4 | semidirect |
| 44. #11924017 | C2×C4 | semidirect |
| 56. C2×C8×C73 | C2×C4 | semidirect |
| 104. C73 | #2949 | semidirect |
| 113. #405 | D73 | semidirect |
| 134. #97 | C2×D73 | semidirect |
| 135. C4×C8 | C2×D73 | semidirect |
| 151. C2×C8 | C4×D73 | semidirect |