Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012062 | C2 | semidirect |
| 3. #26011833 | C2 | semidirect |
| 4. #26011816 | C2 | semidirect |
| 5. #26011737 | C2 | semidirect |
| 6. #26011720 | C2 | semidirect |
| 7. #26011644 | C2 | semidirect |
| 8. #26011632 | C2 | semidirect |
| 9. #408×C173 | C2 | semidirect |
| 10. C22×Dic346 | C22 | semidirect |
| 21. #19149658 | C22 | semidirect |
| 27. #19149638 | C22 | semidirect |
| 28. #19149613 | C22 | semidirect |
| 29. #19149611 | C22 | semidirect |
| 30. #19149604 | C22 | semidirect |
| 31. #19149604 | C22 | semidirect |
| 35. C2×M16×C173 | C22 | semidirect |
| 36. C22×C8×C173 | C22 | semidirect |
| 38. C22⋊C8×C173 | C22 | semidirect |
| 137. C173 | #3200 | semidirect |
| 147. #408 | D173 | semidirect |
| 153. C2×M16 | C2×D173 | semidirect |
| 154. C22×C8 | C2×D173 | semidirect |
| 176. C22⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012062 | 2 |
| #26012055 | 2 |
| #26011833 | 2 |
| #26011816 | 2 |
| #26011737 | 2 |
| #26011720 | 2 |
| #26011644 | 2 |
| #26011632 | 2 |
| #408×C173 | 2 |
| #3200 | 173 |