Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
652 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 213 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 | #391×C73 | C2 |
| socle | C23×C73 | C24 |
| hypercenter | #391 | D73 |
| hypocenter | C73 | C4×#124 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×Dic73 | C2 | semidirect |
| 5. #17988479 | C2 | semidirect |
| 6. #17988452 | C2 | semidirect |
| 7. #17988434 | C2 | semidirect |
| 8. C42×Dic73 | C2 | semidirect |
| 9. #391×C73 | C2 | semidirect |
| 12. #14556580 | C4 | semidirect |
| 44. #11924005 | C2×C4 | semidirect |
| 48. C4×Dic73 | C2×C4 | semidirect |
| 52. C2×Q8×C73 | C2×C4 | semidirect |
| 105. Dic73 | #124 | semidirect |
| 113. C73 | C4×#124 | semidirect |
| 117. #391 | D73 | semidirect |
| 146. C2×Q8 | C4×D73 | semidirect |