Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26013669 | C2 | semidirect |
| 3. #26013668 | C2 | semidirect |
| 4. #26013658 | C2 | semidirect |
| 5. C2×Dic1396 | C2 | semidirect |
| 6. Q16×D349 | C2 | semidirect |
| 7. #26013645 | C2 | semidirect |
| 8. #135×C349 | C2 | semidirect |
| 59. C349 | #578 | semidirect |
| 65. #135 | D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26013686 | 2 |
| #26013669 | 2 |
| #26013668 | 2 |
| #26013658 | 2 |
| C2×Dic1396 | 2 |
| Q16×D349 | 2 |
| #26013645 | 2 |
| #135×C349 | 2 |
| #578 | 349 |