Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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 | #442×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #442 | D73 |
| hypocenter | C73 | #2952 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #442 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17989066 | C2 | semidirect |
| 3. #17988699 | C2 | semidirect |
| 4. #17988695 | C2 | semidirect |
| 5. #17988693 | C2 | semidirect |
| 6. #17988678 | C2 | semidirect |
| 7. C4×#11924016 | C2 | semidirect |
| 8. #106×D73 | C2 | semidirect |
| 9. #17988585 | C2 | semidirect |
| 10. #17988544 | C2 | semidirect |
| 11. #442×C73 | C2 | semidirect |
| 13. #14556610 | C4 | semidirect |
| 41. #11924027 | C2×C4 | semidirect |
| 48. Dic292 | C2×C4 | semidirect |
| 49. #11924016 | C2×C4 | semidirect |
| 53. C8×D73 | C2×C4 | semidirect |
| 66. D8×C73 | C2×C4 | semidirect |
| 115. C73 | #2952 | semidirect |
| 119. #442 | D73 | semidirect |
| 167. D8 | C4×D73 | semidirect |