Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
360 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 137 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×C4 | C22×D43 |
| commutator | C22×C43 | C2×C42 |
| Fitting | C2×#97×C43 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | C2×#97 | D43 |
| hypocenter | C43 | #1752 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#13063235 | C2 | semidirect |
| 5. #14582654 | C2 | semidirect |
| 6. #14582653 | C2 | semidirect |
| 7. C2×#97×C43 | C2 | semidirect |
| 13. C2×C8×D43 | C4 | semidirect |
| 16. (C2×D43)⋊C8 | C4 | semidirect |
| 78. C8×C43 | C22⋊C4 | semidirect |
| 90. C2×D43 | #97 | semidirect |
| 108. C2×#97 | D43 | semidirect |
| 112. C43 | #1752 | semidirect |
| 185. C8 | (C2×D43)⋊C4 | semidirect |