Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
188 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 188 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. C2×#19150222 | C2 | semidirect |
| 3. #26013618 | C2 | semidirect |
| 4. #26013561 | C2 | semidirect |
| 5. C22⋊C8×C349 | C2 | semidirect |
| 7. C2×Dic698 | C22 | semidirect |
| 12. C4⋊Dic349 | C22 | semidirect |
| 16. C2×C8×C349 | C22 | semidirect |
| 34. C22×C349 | SD16 | semidirect |
| 49. C349 | #450 | semidirect |
| 55. C22⋊C8 | D349 | semidirect |
| 63. C2×C8 | C2×D349 | semidirect |
| 88. C22 | #19150222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1396 | 2 |
| C2×#19150222 | 2 |
| #26013618 | 2 |
| #26013561 | 2 |
| C22⋊C8×C349 | 2 |
| #450 | 349 |