Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1492 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 1063 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D43 |
| commutator | C2×C43 | C24×C4 |
| Fitting | C2×2−1+4×C43 | C2 |
| socle | C22×C43 | C25 |
| hypercenter | C2×2−1+4 | D43 |
| hypocenter | C43 | C4×2−1+4 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C2×2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583382 | C2 | semidirect |
| 2. #14583377 | C2 | semidirect |
| 3. #41×Dic43 | C2 | semidirect |
| 4. C2×Q8×Dic43 | C2 | semidirect |
| 14. 2−1+4×C43 | C4 | semidirect |
| 17. #41×C43 | C2×C4 | semidirect |
| 18. C2×Q8×C43 | C2×C4 | semidirect |
| 46. Dic43 | 2−1+4 | direct (N × H) |
| 57. C43 | C4×2−1+4 | semidirect |
| 58. 2−1+4 | Dic43 | direct (N × H) |
| 69. #41 | C2×Dic43 | semidirect |
| 70. C2×Q8 | C2×Dic43 | semidirect |