Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
924 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 237 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 | C22×C73 | C23×C4 |
| Fitting | #390×C73 | C2 |
| socle | C23×C73 | C24 |
| hypercenter | #390 | D73 |
| hypocenter | C73 | C4×#127 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×D4×Dic73 | C2 | semidirect |
| 3. C2×#14556553 | C2 | semidirect |
| 4. C2×#14556551 | C2 | semidirect |
| 5. #17988489 | C2 | semidirect |
| 6. #17988487 | C2 | semidirect |
| 7. #17988456 | C2 | semidirect |
| 8. C42×Dic73 | C2 | semidirect |
| 9. #390×C73 | C2 | semidirect |
| 14. #14556587 | C4 | semidirect |
| 34. C2×D292 | C2×C4 | semidirect |
| 37. C2×C22⋊D73 | C2×C4 | semidirect |
| 52. C4×Dic73 | C2×C4 | semidirect |
| 53. C4×Dic73 | D4 | semidirect |
| 54. C4×Dic73 | D4 | semidirect |
| 58. C2×D4×C73 | C2×C4 | semidirect |
| 115. C4×C73 | C4×D4 | semidirect |
| 118. Dic73 | C4×D4 | semidirect |
| 119. Dic73 | #127 | semidirect |
| 128. C73 | C4×#127 | semidirect |
| 135. #390 | D73 | semidirect |
| 169. C2×D4 | C4×D73 | semidirect |
| 247. C4 | #14556551 | semidirect |