Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
402 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#64408 |
| commutator, socle | C22×C73 | C23×C4 |
| Fitting | #123×C73 | C4 |
| hypercenter | #123 | #64408 |
| hypocenter | C73 | #2978 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989621 | C2 | semidirect |
| 2. #17989620 | C2 | semidirect |
| 3. #17989617 | C2 | semidirect |
| 4. #17989616 | C2 | semidirect |
| 5. #17989611 | C2 | semidirect |
| 6. #17989561 | C2 | semidirect |
| 7. #17989560 | C2 | semidirect |
| 8. #17989558 | C2 | semidirect |
| 12. C2×#11924038 | C22 | semidirect |
| 13. C2×#11924037 | C22 | semidirect |
| 14. C2×#11924036 | C22 | semidirect |
| 15. C22×#10596833 | C22 | semidirect |
| 16. #14556658 | C22 | semidirect |
| 17. C4⋊#10596833 | C22 | semidirect |
| 20. #14556648 | C22 | semidirect |
| 23. C22⋊#10596833 | C22 | semidirect |
| 24. #14556646 | C22 | semidirect |
| 25. C4×#10596833 | C22 | semidirect |
| 133. C73 | #2978 | semidirect |