Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
668 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 157 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 | #380×C73 | C2 |
| hypercenter | #380 | D73 |
| hypocenter | C73 | #2626 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556570 | C2 | semidirect |
| 3. #17988524 | C2 | semidirect |
| 4. #17988509 | C2 | semidirect |
| 5. #17988500 | C2 | semidirect |
| 6. #17988462 | C2 | semidirect |
| 8. #380×C73 | C2 | semidirect |
| 10. C22×Dic146 | C22 | semidirect |
| 13. C2×C4⋊Dic73 | C22 | semidirect |
| 14. C2×C4⋊Dic73 | C22 | semidirect |
| 15. C2×#11924007 | C22 | semidirect |
| 22. #14556498 | C22 | semidirect |
| 24. C2×C4⋊C4×C73 | C22 | semidirect |
| 26. #95×C73 | C22 | semidirect |
| 31. C23×D73 | Q8 | semidirect |
| 118. C73 | #2626 | semidirect |
| 125. #380 | D73 | semidirect |
| 135. C2×C4⋊C4 | C2×D73 | semidirect |
| 144. #95 | C2×D73 | semidirect |