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. #26011785 | C2 | semidirect |
| 4. #26011779 | C2 | semidirect |
| 5. #26011777 | C2 | semidirect |
| 6. #26011773 | C2 | semidirect |
| 7. #26011771 | C2 | semidirect |
| 8. #26011532 | C2 | semidirect |
| 9. #26011513 | C2 | semidirect |
| 11. #474×C173 | C2 | semidirect |
| 44. #14583825 | Q8 | semidirect |
| 86. Dic346 | C2×Q8 | semidirect |
| 105. D4×C173 | C2×Q8 | semidirect |
| 137. C173 | #3079 | semidirect |
| 146. #474 | D173 | semidirect |
| 229. D4 | 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×#14583825 | 2 |
| #26011785 | 2 |
| #26011779 | 2 |
| #26011777 | 2 |
| #26011773 | 2 |
| #26011771 | 2 |
| #26011532 | 2 |
| #26011513 | 2 |
| #26011489 | 2 |
| #474×C173 | 2 |
| #3079 | 173 |