Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
696 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C22×C42×C43 | C2 |
| hypercenter | C22×C42 | D43 |
| hypocenter | C43 | #2850 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063313 | C2 | semidirect |
| 2. C2×#13063304 | C2 | semidirect |
| 4. #14582805 | C2 | semidirect |
| 5. #14582801 | C2 | semidirect |
| 6. #14582790 | C2 | semidirect |
| 7. #14582778 | C2 | semidirect |
| 8. #14582765 | C2 | semidirect |
| 9. C22×C42×C43 | C2 | semidirect |
| 56. C42×C43 | D4 | semidirect |
| 103. C22×C43 | #124 | semidirect |
| 132. C22×C42 | D43 | semidirect |
| 138. C43 | #2850 | semidirect |
| 192. C42 | C22⋊D43 | semidirect |
| 237. C22 | #13063313 | semidirect |