Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
118 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 41 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. #26013638 | C2 | semidirect |
| 3. #26013561 | C2 | semidirect |
| 4. #26013560 | C2 | semidirect |
| 5. #26013559 | C2 | semidirect |
| 6. C8×Dic349 | C2 | semidirect |
| 7. #102×C349 | C2 | semidirect |
| 53. C349 | #486 | semidirect |
| 60. #102 | D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26013638 | 2 |
| #26013635 | 2 |
| #26013561 | 2 |
| #26013560 | 2 |
| #26013559 | 2 |
| C8×Dic349 | 2 |
| #102×C349 | 2 |
| #486 | 349 |