Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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. Q8×D172 | C2 | semidirect |
| 2. #14583309 | C2 | semidirect |
| 3. #14583295 | C2 | semidirect |
| 4. #14583196 | C2 | semidirect |
| 5. #14583189 | C2 | semidirect |
| 6. #14583186 | C2 | semidirect |
| 7. #14583179 | C2 | semidirect |
| 8. #14583030 | C2 | semidirect |
| 11. C43×#554 | C2 | semidirect |
| 63. #10621882 | Q8 | semidirect |
| 78. D4×C43 | C2×Q8 | semidirect |
| 98. C43⋊C8 | C2×Q8 | semidirect |
| 122. #554 | D43 | semidirect |
| 133. C43 | #3384 | semidirect |
| 204. D4 | Q8×D43 | semidirect |