Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
| 3. #14583250 | C2 | semidirect |
| 4. #14583231 | C2 | semidirect |
| 5. #14583184 | C2 | semidirect |
| 6. #14583127 | C2 | semidirect |
| 7. #14583104 | C2 | semidirect |
| 8. #14583036 | C2 | semidirect |
| 9. C8×D172 | C2 | semidirect |
| 10. #103×D43 | C2 | semidirect |
| 11. C4×SD16×C43 | C2 | semidirect |
| 80. Q8×C43 | #41 | semidirect |
| 94. D172 | SD16 | semidirect |
| 137. C4×SD16 | D43 | semidirect |
| 140. C43 | #3298 | semidirect |
| 213. Q8 | #10621898 | semidirect |