Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
316 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 73 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. #14582955 | C2 | semidirect |
| 3. C4×#10621872 | C2 | semidirect |
| 4. #14582628 | C2 | semidirect |
| 5. D4⋊(C43⋊C8) | C2 | semidirect |
| 6. #14582626 | C2 | semidirect |
| 7. C43×D4⋊C8 | C2 | semidirect |
| 19. C4⋊(C43⋊C8) | C22 | semidirect |
| 23. C4×C43⋊C8 | C22 | semidirect |
| 25. C4⋊C8×C43 | C22 | semidirect |
| 26. C4×C8×C43 | C22 | semidirect |
| 66. D4×C43 | M16 | semidirect |
| 80. D172 | M16 | semidirect |
| 128. D4⋊C8 | D43 | semidirect |
| 129. C43 | #1490 | semidirect |
| 143. C4⋊C8 | C2×D43 | semidirect |
| 148. C4×C8 | C2×D43 | semidirect |
| 191. D4 | #10621872 | semidirect |