Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D43 |
| commutator | C22×C43 | C23×C4 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C23×C8×C43 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | C23×C8 | D43 |
| hypocenter | C43 | C2×#408 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#10621877 | C2 | semidirect |
| 3. #14582865 | C2 | direct (N × H) |
| 4. C2×(C2×D43)⋊C8 | C2 | semidirect |
| 5. C23×C8×C43 | C2 | semidirect |
| 15. C2×#10621877 | C22 | semidirect |
| 17. (C2×D43)⋊C8 | C22 | semidirect |
| 21. C22×C8×C43 | C22 | semidirect |
| 92. C2×C43 | #408 | semidirect |
| 98. C23×C8 | D43 | semidirect |
| 101. C43 | C2×#408 | semidirect |
| 116. C22×C8 | C2×D43 | semidirect |
| 188. C2 | #14582865 | direct (N × H) |