Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
446 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26012038 | C2 | semidirect |
| 2. #26011888 | C2 | semidirect |
| 3. #26011866 | C2 | semidirect |
| 4. #26011836 | C2 | semidirect |
| 5. #26011745 | C2 | semidirect |
| 6. #26011743 | C2 | semidirect |
| 7. #26011741 | C2 | semidirect |
| 8. #26011604 | C2 | semidirect |
| 9. #26011601 | C2 | semidirect |
| 10. #26011443 | C2 | semidirect |
| 11. #442×C173 | C2 | semidirect |
| 87. #13063436 | #41 | semidirect |
| 96. C8×C173 | #41 | semidirect |
| 118. C173 | #3184 | semidirect |
| 129. #442 | D173 | semidirect |
| 215. C8 | #14583826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012038 | 2 |
| #26011888 | 2 |
| #26011866 | 2 |
| #26011836 | 2 |
| #26011745 | 2 |
| #26011743 | 2 |
| #26011741 | 2 |
| #26011604 | 2 |
| #26011601 | 2 |
| #26011443 | 2 |
| #442×C173 | 2 |
| #3184 | 173 |