Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D292 |
| commutator | C2×C4×C73 | C24 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #423×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #423 | D73 |
| hypocenter | C73 | #3038 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #423 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556619 | C2 | semidirect |
| 2. C2×#14556588 | C2 | semidirect |
| 3. C4×#11924028 | C2 | semidirect |
| 4. #17988788 | C2 | semidirect |
| 5. #17988783 | C2 | semidirect |
| 6. #17988593 | C2 | semidirect |
| 7. #423×C73 | C2 | semidirect |
| 12. C2×#11924017 | C22 | semidirect |
| 13. C2×D584 | C22 | semidirect |
| 17. C4×Dic146 | C22 | semidirect |
| 18. C4×D292 | C22 | semidirect |
| 23. #14556513 | C22 | semidirect |
| 26. C4⋊C8×C73 | C22 | semidirect |
| 29. #11924028 | D4 | semidirect |
| 78. D292 | C2×D4 | semidirect |
| 82. Dic146 | C2×D4 | semidirect |
| 94. C4×C73 | AGL(1,ℤ/8) | semidirect |
| 105. C73 | #3038 | semidirect |
| 111. #423 | D73 | semidirect |
| 130. C4⋊C8 | C2×D73 | semidirect |
| 201. C4 | #14556619 | semidirect |