Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D73 |
| commutator | C2×C4×C73 | C24 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #500×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #500 | D73 |
| hypocenter | C73 | #3175 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #500 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989211 | C2 | semidirect |
| 2. #17988971 | C2 | semidirect |
| 3. #17988949 | C2 | semidirect |
| 4. #17988834 | C2 | semidirect |
| 5. #17988829 | C2 | semidirect |
| 7. #17988686 | C2 | semidirect |
| 8. #17988681 | C2 | semidirect |
| 9. #17988669 | C2 | semidirect |
| 10. #17988541 | C2 | semidirect |
| 11. #500×C73 | C2 | semidirect |
| 118. C73 | #3175 | semidirect |
| 120. #500 | D73 | semidirect |