Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
914 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 173 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 | C2×#95×C43 | C2 |
| hypercenter | C2×#95 | D43 |
| hypocenter | C43 | #2430 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#10621898 | C2 | semidirect |
| 2. C2×#13063308 | C2 | semidirect |
| 3. C2×#13063299 | C2 | semidirect |
| 4. #14582820 | C2 | semidirect |
| 5. #14582817 | C2 | semidirect |
| 6. #14582812 | C2 | semidirect |
| 7. #14582809 | C2 | semidirect |
| 8. #14582778 | C2 | semidirect |
| 9. #14582777 | C2 | semidirect |
| 10. #14582773 | C2 | semidirect |
| 11. C2×#95×C43 | C2 | semidirect |
| 46. C22×C4×C43 | D4 | semidirect |
| 55. C2×C22⋊D43 | D4 | semidirect |
| 110. C2×C4×C43 | #41 | semidirect |
| 176. C2×#95 | D43 | semidirect |
| 177. C43 | #2430 | semidirect |
| 232. C22×C4 | D172 | semidirect |
| 292. C2×C4 | #10621898 | semidirect |