Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
944 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C43×#395 | C2 |
| hypercenter | #395 | D43 |
| hypocenter | C43 | #2388 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #395 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#10621902 | C2 | semidirect |
| 2. C2×#13063287 | C2 | semidirect |
| 3. #14582816 | C2 | semidirect |
| 4. #14582810 | C2 | semidirect |
| 5. #14582809 | C2 | semidirect |
| 6. #14582746 | C2 | semidirect |
| 7. C43×#395 | C2 | semidirect |
| 38. C2×C4×D43 | D4 | semidirect |
| 52. C22×D43 | #41 | semidirect |
| 59. C2×C4×C43 | #41 | semidirect |
| 91. #395 | D43 | semidirect |
| 96. C43 | #2388 | semidirect |
| 155. C2×C4 | #10621902 | semidirect |