Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
274 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #14582817 |
| commutator | C22×C4×C43 | C23 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#344 | C2 |
| socle | C2×C43 | #394 |
| hypercenter | #344 | D43 |
| hypocenter | C43 | #2048 |
| LCS | G ▷ C22×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #344 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14582947 | C2 | semidirect |
| 3. #14582917 | C2 | semidirect |
| 4. #14582903 | C2 | semidirect |
| 5. #14582881 | C2 | semidirect |
| 6. C2×#13063241 | C2 | semidirect |
| 7. C43×#344 | C2 | semidirect |
| 117. #344 | D43 | semidirect |
| 118. C43 | #2048 | semidirect |