Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D344 | C2 | semidirect |
| 2. C2×#13063322 | C2 | semidirect |
| 3. C2×C4×D172 | C2 | semidirect |
| 4. #14583095 | C2 | direct (N × H) |
| 5. C2×#13063247 | C2 | semidirect |
| 6. C2×C4⋊C8×C43 | C2 | semidirect |
| 13. C2×D344 | C22 | semidirect |
| 15. #13063322 | C22 | semidirect |
| 17. C4×D172 | C22 | semidirect |
| 20. #13063247 | C22 | semidirect |
| 23. C4⋊C8×C43 | C22 | semidirect |
| 39. C2×D172 | D4 | semidirect |
| 62. C2×C4×C43 | D8 | semidirect |
| 78. D172 | C2×D4 | semidirect |
| 95. C4×C43 | C2×D8 | semidirect |
| 100. C2×C43 | #459 | semidirect |
| 110. C2×C4⋊C8 | D43 | semidirect |
| 112. C43 | C2×#459 | semidirect |
| 128. C4⋊C8 | C2×D43 | semidirect |
| 179. C2×C4 | D344 | semidirect |
| 202. C4 | C2×D344 | semidirect |
| 207. C2 | #14583095 | direct (N × H) |