Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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×Q8×D349 | C2 | semidirect |
| 3. #26013637 | C2 | semidirect |
| 4. #26013628 | C2 | semidirect |
| 5. #26013627 | C2 | semidirect |
| 6. #26013624 | C2 | semidirect |
| 7. #26013617 | C2 | semidirect |
| 8. #26013596 | C2 | semidirect |
| 9. C4⋊Q8×C349 | C2 | semidirect |
| 63. C349 | #536 | semidirect |
| 68. C4⋊Q8 | D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150234 | 2 |
| C2×Q8×D349 | 2 |
| #26013637 | 2 |
| #26013628 | 2 |
| #26013627 | 2 |
| #26013624 | 2 |
| #26013617 | 2 |
| #26013596 | 2 |
| C4⋊Q8×C349 | 2 |
| #536 | 349 |