Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 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. C4⋊Q8×D173 | C2 | semidirect |
| 3. #26011784 | C2 | semidirect |
| 4. #26011780 | C2 | semidirect |
| 5. #26011776 | C2 | semidirect |
| 6. #26011772 | C2 | semidirect |
| 7. #26011768 | C2 | semidirect |
| 8. #26011530 | C2 | semidirect |
| 9. #26011513 | C2 | semidirect |
| 11. #475×C173 | C2 | semidirect |
| 44. #14583827 | Q8 | semidirect |
| 88. D692 | C2×Q8 | semidirect |
| 105. Q8×C173 | C2×Q8 | semidirect |
| 137. C173 | #3079 | semidirect |
| 144. #475 | D173 | semidirect |
| 226. Q8 | Q8×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D173 | 2 |
| C4×#14583827 | 2 |
| #26011784 | 2 |
| #26011780 | 2 |
| #26011776 | 2 |
| #26011772 | 2 |
| #26011768 | 2 |
| #26011530 | 2 |
| #26011513 | 2 |
| #26011491 | 2 |
| #475×C173 | 2 |
| #3079 | 173 |