Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
988 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 988 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D43 |
| commutator, socle | C22×C43 | C25 |
| Fitting | C4×#41×C43 | C2 |
| hypercenter | C4×#41 | D43 |
| hypocenter | C43 | #3504 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583625 | C2 | semidirect |
| 2. #14583608 | C2 | semidirect |
| 3. #14583527 | C2 | semidirect |
| 4. #14583456 | C2 | semidirect |
| 5. C2×#13063317 | C2 | semidirect |
| 28. #41×C43 | Q8 | semidirect |
| 82. C43 | #3504 | semidirect |
| 103. #41 | Dic86 | semidirect |