Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
534 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 141 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 | C4×C4⋊C4×C43 | C2 |
| hypercenter | C4×C4⋊C4 | D43 |
| hypocenter | C43 | #2662 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063319 | C2 | semidirect |
| 2. C2×#13063313 | C2 | semidirect |
| 3. #14582821 | C2 | semidirect |
| 4. #14582820 | C2 | semidirect |
| 5. #14582817 | C2 | semidirect |
| 6. #14582816 | C2 | semidirect |
| 7. #14582812 | C2 | semidirect |
| 9. #14582801 | C2 | semidirect |
| 10. #14582790 | C2 | semidirect |
| 11. C4×C4⋊C4×C43 | C2 | semidirect |
| 57. C42×C43 | D4 | semidirect |
| 154. C4×C4⋊C4 | D43 | semidirect |
| 155. C43 | #2662 | semidirect |
| 214. C42 | D172 | semidirect |