Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
568 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D43 |
| commutator, socle | C23×C43 | C24 |
| Frattini | C23 | C23×D43 |
| Fitting | C2×C4×Q8×C43 | C2 |
| hypercenter | C2×C4×Q8 | D43 |
| hypocenter | C43 | #2398 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14582838 | C2 | semidirect |
| 3. #14582825 | C2 | semidirect |
| 5. #14582810 | C2 | semidirect |
| 6. C4×(C2×D43)⋊C4 | C2 | semidirect |
| 7. #14582745 | C2 | semidirect |
| 8. C2×C4×Q8×C43 | C2 | semidirect |
| 97. C2×C4×Q8 | D43 | semidirect |
| 105. C43 | #2398 | semidirect |