Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
180 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D43 |
| commutator | C4×C43 | C22×C8 |
| Frattini | C42 | C22×D43 |
| Fitting | C43×#335 | C2 |
| socle | C22×C43 | C2×C4⋊C4 |
| hypercenter | #335 | D43 |
| hypocenter | C43 | #1565 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ #335 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #14582651 | C2 | semidirect |
| 5. #14582650 | C2 | semidirect |
| 6. #14582649 | C2 | semidirect |
| 7. C43×#335 | C2 | semidirect |
| 39. #10621872 | C8 | semidirect |
| 56. C8×C43 | C2×C8 | semidirect |
| 60. C43⋊C8 | C2×C8 | semidirect |
| 82. #335 | D43 | semidirect |
| 85. C43 | #1565 | semidirect |
| 138. C8 | C8×D43 | semidirect |