Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
820 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 253 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 | C22×C43 | C23×C4 |
| Fitting | C43×#380 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #380 | D43 |
| hypocenter | C43 | Q8×C22⋊C4 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13063290 | C2 | semidirect |
| 3. #14582804 | C2 | semidirect |
| 4. #14582803 | C2 | semidirect |
| 10. C22×Dic86 | C4 | semidirect |
| 50. C22⋊Dic43 | Q8 | semidirect |
| 78. C2×Dic43 | C2×Q8 | semidirect |
| 81. Dic86 | C22⋊C4 | semidirect |
| 86. C22×C43 | C4×Q8 | semidirect |
| 114. C43 | Q8×C22⋊C4 | semidirect |
| 192. C22 | #13063290 | semidirect |