Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
280 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D43 |
| commutator, socle | C23×C43 | C22×C4 |
| Fitting | C43×#336 | C2 |
| hypercenter | #336 | D43 |
| hypocenter | C43 | #1924 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊(C43⋊C8) | C2 | semidirect |
| 4. C2×#13063235 | C2 | semidirect |
| 6. #14582653 | C2 | semidirect |
| 7. C43×#336 | C2 | semidirect |
| 129. #336 | D43 | semidirect |
| 130. C43 | #1924 | semidirect |