Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 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. #26013604 | C2 | semidirect |
| 4. #26013562 | C2 | semidirect |
| 6. C8×Dic349 | C2 | semidirect |
| 7. #106×C349 | C2 | semidirect |
| 11. #19150222 | C4 | semidirect |
| 22. Dic698 | C2×C4 | semidirect |
| 33. C8×C349 | C2×C4 | semidirect |
| 44. Dic349 | SD16 | semidirect |
| 49. C349 | C4×SD16 | semidirect |
| 54. #106 | D349 | semidirect |
| 83. C8 | C4×D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150222 | 2 |
| #26013604 | 2 |
| #26013601 | 2 |
| #26013562 | 2 |
| #26013559 | 2 |
| C8×Dic349 | 2 |
| #106×C349 | 2 |
| C4×SD16 | 349 |