Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
480 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 480 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 |
|---|---|---|
| 2. #14583176 | C2 | direct (N × H) |
| 3. C2×#13063258 | C2 | semidirect |
| 4. C2×C4⋊(C43⋊C8) | C2 | semidirect |
| 6. C2×C4⋊Q8×C43 | C2 | semidirect |
| 14. #13063258 | C22 | semidirect |
| 15. C4⋊(C43⋊C8) | C22 | semidirect |
| 19. C4⋊Q8×C43 | C22 | semidirect |
| 33. C2×D172 | Q8 | semidirect |
| 67. D172 | C2×Q8 | semidirect |
| 86. C2×C43 | #474 | semidirect |
| 91. C2×C4⋊Q8 | D43 | semidirect |
| 97. C43 | C2×#474 | semidirect |
| 103. C4⋊Q8 | C2×D43 | semidirect |
| 177. C2 | #14583176 | direct (N × H) |