Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#496 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #496 | D43 |
| hypocenter | C43 | #3219 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #496 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583447 | C2 | semidirect |
| 2. #14583428 | C2 | semidirect |
| 3. #14583294 | C2 | semidirect |
| 4. #14583268 | C2 | semidirect |
| 5. #14583263 | C2 | semidirect |
| 6. #14583119 | C2 | semidirect |
| 7. #14583112 | C2 | semidirect |
| 8. #14583058 | C2 | semidirect |
| 9. #14583041 | C2 | semidirect |
| 10. #14582954 | C2 | semidirect |
| 11. C43×#496 | C2 | semidirect |
| 144. #496 | D43 | semidirect |
| 152. C43 | #3219 | semidirect |