Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
254 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #14582814 |
| commutator | C22×C4×C43 | C23 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#419 | C2 |
| socle | C2×C43 | #394 |
| hypercenter | #419 | D43 |
| hypocenter | C43 | #2049 |
| LCS | G ▷ C22×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #419 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14582947 | C2 | semidirect |
| 5. C2×#13063244 | C2 | semidirect |
| 6. #14582669 | C2 | semidirect |
| 7. C43×#419 | C2 | semidirect |
| 109. #419 | D43 | semidirect |
| 113. C43 | #2049 | semidirect |