Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
724 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 151 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×#398 | C2 |
| hypercenter | #398 | D43 |
| hypocenter | C43 | #2543 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #398 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063300 | C2 | semidirect |
| 2. C2×#13063300 | C2 | semidirect |
| 3. C2×#13063287 | C2 | semidirect |
| 4. #14582825 | C2 | semidirect |
| 5. #14582816 | C2 | semidirect |
| 6. #14582809 | C2 | semidirect |
| 7. #14582789 | C2 | semidirect |
| 8. #14582777 | C2 | semidirect |
| 9. #14582777 | C2 | semidirect |
| 10. #95×D43 | C2 | semidirect |
| 11. C43×#398 | C2 | semidirect |
| 59. C2×D172 | D4 | semidirect |
| 66. C2×C4×D43 | D4 | semidirect |
| 165. #398 | D43 | semidirect |
| 173. C43 | #2543 | semidirect |