Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13063294 |
| commutator | C42×C43 | C23 |
| Frattini | C42 | C22×D43 |
| Fitting | C43×#556 | C2 |
| socle | C22×C43 | #120 |
| hypercenter | #556 | D43 |
| hypocenter | C43 | #1628 |
| LCS | G ▷ C42×C43 ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #556 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583247 | C2 | semidirect |
| 2. #14583099 | C2 | semidirect |
| 4. #14582645 | C2 | semidirect |
| 5. Q8⋊(C43⋊C8) | C2 | semidirect |
| 6. D4⋊(C43⋊C8) | C2 | semidirect |
| 7. C43×#556 | C2 | semidirect |
| 96. #556 | D43 | semidirect |
| 103. C43 | #1628 | semidirect |