Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
106 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 2. #26013645 | C2 | semidirect |
| 3. #26013574 | C2 | semidirect |
| 4. #26013566 | C2 | semidirect |
| 5. #26013565 | C2 | semidirect |
| 6. C8×Dic349 | C2 | semidirect |
| 7. #131×C349 | C2 | semidirect |
| 9. #19150223 | C4 | semidirect |
| 10. #19150221 | C4 | semidirect |
| 11. #19150220 | C4 | semidirect |
| 12. #19150218 | C4 | semidirect |
| 51. C349 | #443 | semidirect |
| 55. #131 | D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26013659 | 2 |
| #26013645 | 2 |
| #26013574 | 2 |
| #26013566 | 2 |
| #26013565 | 2 |
| C8×Dic349 | 2 |
| #131×C349 | 2 |
| #443 | 349 |