Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
348 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 129 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 | #1753 |
| 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 |
|---|---|---|
| 3. C2×#13063235 | C2 | semidirect |
| 4. C2×C4×C43⋊C8 | C2 | semidirect |
| 6. #14582653 | C2 | semidirect |
| 7. C43×#336 | C2 | semidirect |
| 11. C2×#10621872 | C4 | semidirect |
| 16. (C2×D43)⋊C8 | C4 | semidirect |
| 60. C2×C4×C43 | M16 | semidirect |
| 80. C43⋊C8 | C22⋊C4 | semidirect |
| 111. #336 | D43 | semidirect |
| 112. C43 | #1753 | semidirect |
| 175. C2×C4 | #10621872 | semidirect |