Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
284 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13063300 |
| commutator | C2×C4×C43 | C22×C4 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#427 | C2 |
| socle | C2×C43 | #390 |
| hypercenter | #427 | D43 |
| hypocenter | C43 | #1976 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #427 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14582917 | C2 | semidirect |
| 3. #14582872 | C2 | semidirect |
| 4. #14582854 | C2 | semidirect |
| 5. C43×#427 | C2 | semidirect |
| 11. C2×Dic172 | C4 | semidirect |
| 12. C2×#10621873 | C4 | semidirect |
| 13. C2×D344 | C4 | semidirect |
| 98. #427 | D43 | semidirect |
| 102. C43 | #1976 | semidirect |