Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
576 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 145 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×#376 | C2 |
| hypercenter | #376 | D43 |
| hypocenter | C43 | #2610 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063313 | C2 | semidirect |
| 2. C2×#13063282 | C2 | semidirect |
| 3. #14582820 | C2 | semidirect |
| 4. #14582817 | C2 | semidirect |
| 5. #14582812 | C2 | semidirect |
| 7. #14582801 | C2 | semidirect |
| 8. #14582791 | C2 | semidirect |
| 9. #14582790 | C2 | semidirect |
| 10. #14582777 | C2 | semidirect |
| 11. C43×#376 | C2 | semidirect |
| 59. C42×C43 | D4 | semidirect |
| 156. #376 | D43 | semidirect |
| 157. C43 | #2610 | semidirect |
| 217. C42 | D172 | semidirect |