Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
412 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 412 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 | 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 | #1749 |
| 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×#13063236 | C2 | semidirect |
| 4. #14582653 | C2 | semidirect |
| 5. C2×#97×C43 | C2 | semidirect |
| 13. (C2×D43)⋊C8 | C4 | semidirect |
| 32. C2×C8×C43 | C2×C4 | semidirect |
| 40. C2×C43⋊C8 | C2×C4 | semidirect |
| 74. C2×D43 | #97 | semidirect |
| 90. C2×#97 | D43 | semidirect |
| 92. C43 | #1749 | semidirect |
| 122. C2×C8 | C4×D43 | semidirect |