Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19149726 | C2 | semidirect |
| 2. C2×#19149707 | C2 | semidirect |
| 3. C22×#14583815 | C2 | semidirect |
| 4. #26012055 | C2 | semidirect |
| 5. #26011638 | C2 | semidirect |
| 6. #26011632 | C2 | semidirect |
| 7. #26011501 | C2 | semidirect |
| 8. #26011488 | C2 | semidirect |
| 9. #408×C173 | C2 | semidirect |
| 13. C2×#14583826 | C22 | semidirect |
| 17. C22×Dic346 | C22 | semidirect |
| 30. #19149604 | C22 | semidirect |
| 31. #19149604 | C22 | semidirect |
| 32. #19149601 | C22 | semidirect |
| 36. C22⋊C8×C173 | C22 | semidirect |
| 41. #14583826 | D4 | semidirect |
| 49. C2×Dic346 | D4 | semidirect |
| 145. C173 | #3010 | semidirect |
| 155. #408 | D173 | semidirect |
| 182. C22⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149726 | 2 |
| C2×#19149707 | 2 |
| C22×#14583815 | 2 |
| #26012055 | 2 |
| #26011638 | 2 |
| #26011632 | 2 |
| #26011501 | 2 |
| #26011488 | 2 |
| #408×C173 | 2 |
| #3010 | 173 |