Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
128 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13063283 |
| commutator | C2×C4×C43 | C22×C4 |
| Frattini | C2×C8 | C22×D43 |
| Fitting | C43×#364 | C2 |
| socle | C2×C43 | #432 |
| hypercenter | #364 | D43 |
| hypocenter | C43 | #2165 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ C2×C8 ◁ #364 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14582720 | C2 | semidirect |
| 4. #14582676 | C2 | semidirect |
| 5. C43×#364 | C2 | semidirect |
| 56. #364 | D43 | semidirect |
| 59. C43 | #2165 | semidirect |