Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
150 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 3. #26013702 | C2 | semidirect |
| 12. C2×Dic698 | C4 | semidirect |
| 15. Q8×D349 | C4 | semidirect |
| 19. C2×Q8×C349 | C4 | semidirect |
| 54. C349 | #419 | semidirect |
| 66. C2×Q8 | #13063703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D349⋊M16 | 2 |
| #26013718 | 2 |
| #26013702 | 2 |
| C2×Q8×D349 | 2 |
| #419 | 349 |