Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4⋊Q8×D173 | C2 | semidirect |
| 3. #26011853 | C2 | semidirect |
| 4. #26011851 | C2 | semidirect |
| 5. #26011850 | C2 | semidirect |
| 6. #26011840 | C2 | semidirect |
| 7. #26011836 | C2 | semidirect |
| 8. #26011491 | C2 | semidirect |
| 9. #26011489 | C2 | semidirect |
| 10. #26011443 | C2 | semidirect |
| 11. #489×C173 | C2 | semidirect |
| 140. C173 | #3141 | semidirect |
| 147. #489 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012040 | 2 |
| C4⋊Q8×D173 | 2 |
| #26011853 | 2 |
| #26011851 | 2 |
| #26011850 | 2 |
| #26011840 | 2 |
| #26011836 | 2 |
| #26011491 | 2 |
| #26011489 | 2 |
| #26011443 | 2 |
| #489×C173 | 2 |
| #3141 | 173 |