Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
402 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D43 |
| commutator, socle | C22×C43 | C23×C4 |
| Fitting | C43×#525 | C2 |
| hypercenter | #525 | D43 |
| hypocenter | C43 | #2978 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14582977 | C2 | semidirect |
| 2. #14582971 | C2 | semidirect |
| 3. #14582960 | C2 | semidirect |
| 4. #14582866 | C2 | semidirect |
| 5. #14582863 | C2 | semidirect |
| 8. C2×#10621877 | C22 | semidirect |
| 9. C22×C43⋊C8 | C22 | semidirect |
| 10. C4⋊(C43⋊C8) | C22 | semidirect |
| 14. C22⋊(C43⋊C8) | C22 | semidirect |
| 15. #13063236 | C22 | semidirect |
| 16. C4×C43⋊C8 | C22 | semidirect |
| 96. C43 | #2978 | semidirect |