Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
426 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 426 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583571 | C2 | semidirect |
| 2. #14583247 | C2 | semidirect |
| 3. #14583176 | C2 | semidirect |
| 4. #14583094 | C2 | semidirect |
| 5. Q8×C43⋊C8 | C2 | semidirect |
| 6. C4×#10621882 | C2 | semidirect |
| 7. D4×Q8×C43 | C2 | semidirect |
| 47. Q8×C43 | D8 | semidirect |
| 49. D4×C43 | #41 | semidirect |
| 83. D4×Q8 | D43 | semidirect |
| 89. C43 | #3358 | semidirect |
| 129. Q8 | #10621882 | semidirect |
| 135. D4 | #10621902 | semidirect |