Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26013634 | C2 | semidirect |
| 2. #26013630 | C2 | semidirect |
| 3. #26013628 | C2 | semidirect |
| 4. #26013623 | C2 | semidirect |
| 6. Q8×Dic349 | C2 | semidirect |
| 7. #26013601 | C2 | semidirect |
| 8. #26013599 | C2 | semidirect |
| 9. #26013597 | C2 | semidirect |
| 10. C2×C4×Dic349 | C2 | semidirect |
| 11. C22⋊Q8×C349 | C2 | semidirect |
| 74. C349 | #529 | semidirect |
| 80. C22⋊Q8 | D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26013634 | 2 |
| #26013630 | 2 |
| #26013628 | 2 |
| #26013623 | 2 |
| #26013613 | 2 |
| Q8×Dic349 | 2 |
| #26013601 | 2 |
| #26013599 | 2 |
| #26013597 | 2 |
| C2×C4×Dic349 | 2 |
| C22⋊Q8×C349 | 2 |
| #529 | 349 |