Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
408 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 105 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 | C2×C22⋊C8×C43 | C2 |
| hypercenter | C2×C22⋊C8 | D43 |
| hypocenter | C43 | #1870 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C22⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#10621872 | C2 | semidirect |
| 3. C2×C22⋊(C43⋊C8) | C2 | semidirect |
| 4. C2×(C2×D43)⋊C8 | C2 | semidirect |
| 5. #14582653 | C2 | semidirect |
| 6. #14582653 | C2 | semidirect |
| 7. C2×C22⋊C8×C43 | C2 | semidirect |
| 54. C2×C8×C43 | D4 | semidirect |
| 65. C2×C43⋊C8 | D4 | semidirect |
| 73. C23×C43 | M16 | semidirect |
| 104. C2×Dic43 | M16 | semidirect |
| 156. C2×C22⋊C8 | D43 | semidirect |
| 159. C43 | #1870 | semidirect |
| 213. C2×C8 | C22⋊D43 | semidirect |
| 232. C23 | #10621872 | semidirect |