Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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×#19150233 | C2 | semidirect |
| 2. #26013672 | C2 | semidirect |
| 3. #26013667 | C2 | semidirect |
| 4. #26013661 | C2 | semidirect |
| 5. C2×M16×C349 | C2 | semidirect |
| 9. #19150233 | C22 | semidirect |
| 10. C2×Dic698 | C22 | semidirect |
| 11. C2×D1396 | C22 | semidirect |
| 14. Dic1396 | C22 | semidirect |
| 15. #19150222 | C22 | semidirect |
| 16. D2792 | C22 | semidirect |
| 18. M16×C349 | C22 | semidirect |
| 19. C2×C8×C349 | C22 | semidirect |
| 49. C349 | #575 | semidirect |
| 55. C2×M16 | D349 | semidirect |
| 68. M16 | C2×D349 | semidirect |
| 69. C2×C8 | C2×D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150233 | 2 |
| #26013672 | 2 |
| #26013667 | 2 |
| #26013661 | 2 |
| C2×M16×C349 | 2 |
| #575 | 349 |