Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
952 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 173 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×#391 | C2 |
| hypercenter | #391 | D43 |
| hypocenter | C43 | #2431 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#10621902 | C2 | semidirect |
| 2. C2×#13063322 | C2 | semidirect |
| 3. C2×#13063314 | C2 | semidirect |
| 4. C2×#13063300 | C2 | semidirect |
| 5. #14582809 | C2 | semidirect |
| 6. #14582800 | C2 | semidirect |
| 7. #14582777 | C2 | semidirect |
| 8. C4×(C2×D43)⋊C4 | C2 | semidirect |
| 9. C43×#391 | C2 | semidirect |
| 38. C2×Q8×C43 | D4 | semidirect |
| 59. C2×D172 | D4 | semidirect |
| 65. C2×C4×D43 | D4 | semidirect |
| 100. C2×C4×C43 | #41 | semidirect |
| 154. #391 | D43 | semidirect |
| 158. C43 | #2431 | semidirect |
| 188. C2×Q8 | D172 | semidirect |
| 262. C2×C4 | #10621902 | semidirect |