Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
564 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 147 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, socle | C23×C73 | C24 |
| Fitting | #399×C73 | C2 |
| hypercenter | #399 | D73 |
| hypocenter | C73 | #2580 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #399 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556556 | C2 | semidirect |
| 3. #17988522 | C2 | semidirect |
| 4. #17988500 | C2 | semidirect |
| 5. #17988499 | C2 | semidirect |
| 7. #17988482 | C2 | semidirect |
| 8. #17988459 | C2 | semidirect |
| 9. #17988458 | C2 | semidirect |
| 10. #17988451 | C2 | semidirect |
| 11. #399×C73 | C2 | semidirect |
| 42. C2×C22⋊D73 | Q8 | semidirect |
| 141. C73 | #2580 | semidirect |
| 145. #399 | D73 | semidirect |