Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
592 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 157 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×#389 | C2 |
| hypercenter | #389 | D43 |
| hypocenter | C43 | #2683 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #389 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063305 | C2 | semidirect |
| 2. C2×#13063303 | C2 | semidirect |
| 3. #14582821 | C2 | semidirect |
| 4. #14582821 | C2 | semidirect |
| 5. #14582820 | C2 | semidirect |
| 7. #14582797 | C2 | semidirect |
| 9. C43×#389 | C2 | semidirect |
| 44. C2×D172 | Q8 | semidirect |
| 53. C4⋊C4×C43 | D4 | semidirect |
| 63. C4⋊Dic43 | D4 | semidirect |
| 139. #389 | D43 | semidirect |
| 141. C43 | #2683 | semidirect |
| 191. C4⋊C4 | D172 | semidirect |