Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
760 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 185 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 | C4×C4⋊C4×C43 | C2 |
| hypercenter | C4×C4⋊C4 | D43 |
| hypocenter | C43 | #2540 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063313 | C2 | semidirect |
| 2. C2×#13063305 | C2 | semidirect |
| 3. C2×#13063300 | C2 | semidirect |
| 4. C2×C4×D172 | C2 | semidirect |
| 5. #14582836 | C2 | semidirect |
| 6. #14582809 | C2 | semidirect |
| 7. #14582801 | C2 | semidirect |
| 8. C4×C4⋊C4×C43 | C2 | semidirect |
| 49. C4⋊C4×C43 | D4 | semidirect |
| 51. C42×C43 | D4 | semidirect |
| 130. C4×C4⋊C4 | D43 | semidirect |
| 131. C43 | #2540 | semidirect |
| 174. C4⋊C4 | D172 | semidirect |
| 181. C42 | D172 | semidirect |