Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
696 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 145 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×#390 | C2 |
| hypercenter | #390 | D43 |
| hypocenter | C43 | #2555 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063311 | C2 | semidirect |
| 2. C2×#13063298 | C2 | semidirect |
| 3. #14582819 | C2 | semidirect |
| 4. #14582816 | C2 | semidirect |
| 5. #14582807 | C2 | semidirect |
| 6. #14582787 | C2 | semidirect |
| 7. #14582775 | C2 | semidirect |
| 8. C4×(C2×D43)⋊C4 | C2 | semidirect |
| 9. C43×#390 | C2 | semidirect |
| 66. (C2×D43)⋊C4 | D4 | semidirect |
| 148. #390 | D43 | semidirect |
| 152. C43 | #2555 | semidirect |