Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
416 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 153 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 | C22×C43 | C2×C42 |
| Fitting | C43×#336 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | #336 | D43 |
| hypocenter | C43 | #1729 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #14582654 | C2 | semidirect |
| 5. #14582653 | C2 | semidirect |
| 6. #14582653 | C2 | semidirect |
| 7. C43×#336 | C2 | semidirect |
| 11. C2×#10621872 | C4 | semidirect |
| 16. C2×C8×D43 | C4 | semidirect |
| 115. #336 | D43 | semidirect |
| 116. C43 | #1729 | semidirect |