Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 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. #26013686 | C2 | semidirect |
| 2. #26013685 | C2 | semidirect |
| 3. #26013672 | C2 | semidirect |
| 4. #26013667 | C2 | semidirect |
| 5. #26013661 | C2 | semidirect |
| 6. C2×#19150222 | C2 | semidirect |
| 7. #131×C349 | C2 | semidirect |
| 10. #19150233 | C22 | semidirect |
| 12. C2×Dic698 | C22 | semidirect |
| 16. Dic1396 | C22 | semidirect |
| 17. #19150222 | C22 | semidirect |
| 18. #19150222 | C22 | semidirect |
| 19. #19150222 | C22 | semidirect |
| 20. D2792 | C22 | semidirect |
| 22. M16×C349 | C22 | semidirect |
| 23. C2×C8×C349 | C22 | semidirect |
| 53. C349 | #577 | semidirect |
| 61. #131 | D349 | semidirect |
| 76. M16 | C2×D349 | semidirect |
| 77. C2×C8 | C2×D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26013686 | 2 |
| #26013685 | 2 |
| #26013672 | 2 |
| #26013667 | 2 |
| #26013661 | 2 |
| C2×#19150222 | 2 |
| #131×C349 | 2 |
| #577 | 349 |