Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
852 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 161 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×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C43×#393 | C2 |
| hypercenter | #393 | D43 |
| hypocenter | C43 | #2436 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q8×D43 | C2 | semidirect |
| 2. C2×#13063311 | C2 | semidirect |
| 4. #14582812 | C2 | semidirect |
| 5. #14582811 | C2 | semidirect |
| 6. #14582810 | C2 | semidirect |
| 7. #14582803 | C2 | semidirect |
| 8. #14582777 | C2 | semidirect |
| 9. #14582775 | C2 | semidirect |
| 10. #14582746 | C2 | semidirect |
| 11. C43×#393 | C2 | semidirect |
| 68. C2×Dic86 | D4 | semidirect |
| 141. C2×D43 | #124 | semidirect |
| 165. #393 | D43 | semidirect |
| 170. C43 | #2436 | semidirect |