Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
422 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D73 |
| commutator, socle | C22×C73 | C23×C4 |
| Fitting | #525×C73 | C2 |
| hypercenter | #525 | D73 |
| hypocenter | C73 | #2977 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17988659 | C2 | semidirect |
| 2. D4×#10596831 | C2 | semidirect |
| 3. #17988648 | C2 | semidirect |
| 4. #17988554 | C2 | semidirect |
| 5. C2×C22⋊#10596831 | C2 | semidirect |
| 7. C2×#11924012 | C22 | semidirect |
| 9. C22×#10596831 | C22 | semidirect |
| 10. C4⋊#10596831 | C22 | semidirect |
| 14. C22⋊#10596831 | C22 | semidirect |
| 15. #14556502 | C22 | semidirect |
| 16. C4×#10596831 | C22 | semidirect |
| 90. C73 | #2977 | semidirect |