Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
442 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 442 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. #26012055 | C2 | semidirect |
| 2. #26011816 | C2 | semidirect |
| 3. #26011744 | C2 | semidirect |
| 4. #26011727 | C2 | semidirect |
| 5. #26011627 | C2 | semidirect |
| 6. #408×C173 | C2 | semidirect |
| 7. C22×D692 | C22 | semidirect |
| 13. #19149653 | C22 | semidirect |
| 16. #19149638 | C22 | semidirect |
| 17. #19149613 | C22 | semidirect |
| 18. #19149611 | C22 | semidirect |
| 19. #19149601 | C22 | semidirect |
| 20. #19149601 | C22 | semidirect |
| 22. C2×M16×C173 | C22 | semidirect |
| 23. C22×C8×C173 | C22 | semidirect |
| 24. C22⋊C8×C173 | C22 | semidirect |
| 92. C173 | #3199 | semidirect |
| 99. #408 | D173 | semidirect |
| 104. C2×M16 | C2×D173 | semidirect |
| 105. C22×C8 | C2×D173 | semidirect |
| 117. C22⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012055 | 2 |
| #26011816 | 2 |
| #26011744 | 2 |
| #26011727 | 2 |
| #26011627 | 2 |
| #408×C173 | 2 |
| #3199 | 173 |