Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
112 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 112 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. C2×Dic1396 | C2 | semidirect |
| 4. C4×Dic698 | C2 | semidirect |
| 5. #26013564 | C2 | semidirect |
| 7. C4⋊C8×C349 | C2 | semidirect |
| 51. C349 | #464 | semidirect |
| 57. C4⋊C8 | D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic1396 | 2 |
| C2×#19150222 | 2 |
| #26013627 | 2 |
| C4×Dic698 | 2 |
| #26013564 | 2 |
| #26013561 | 2 |
| C4⋊C8×C349 | 2 |
| #464 | 349 |