Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
944 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 167 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×#392 | C2 |
| hypercenter | #392 | D43 |
| hypocenter | C43 | #2388 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#10621900 | C2 | semidirect |
| 2. C2×D4×Dic43 | C2 | semidirect |
| 3. C2×(C22⋊D43)⋊C4 | C2 | semidirect |
| 4. #14582820 | C2 | semidirect |
| 5. #14582815 | C2 | semidirect |
| 6. #14582813 | C2 | semidirect |
| 7. #14582811 | C2 | semidirect |
| 8. #14582807 | C2 | semidirect |
| 9. C22⋊C4×Dic43 | C2 | semidirect |
| 10. #14582746 | C2 | semidirect |
| 11. C43×#392 | C2 | semidirect |
| 60. C22×Dic43 | D4 | semidirect |
| 68. C2×C4×D43 | D4 | semidirect |
| 93. C23×C43 | #41 | semidirect |
| 108. C2×C4×C43 | #41 | semidirect |
| 125. C2×Dic43 | #41 | semidirect |
| 175. #392 | D43 | semidirect |
| 178. C43 | #2388 | semidirect |
| 265. C23 | #10621900 | semidirect |
| 294. C2×C4 | #10621900 | semidirect |