Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26013687 | C2 | semidirect |
| 2. #26013686 | C2 | semidirect |
| 3. #26013672 | C2 | semidirect |
| 4. #26013671 | C2 | semidirect |
| 5. #26013668 | C2 | semidirect |
| 6. #26013660 | C2 | semidirect |
| 7. #26013659 | C2 | semidirect |
| 8. C2×#19150223 | C2 | semidirect |
| 9. Q16×D349 | C2 | semidirect |
| 10. #26013647 | C2 | semidirect |
| 11. #137×C349 | C2 | semidirect |
| 87. C349 | #578 | semidirect |
| 94. #137 | D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26013687 | 2 |
| #26013686 | 2 |
| #26013672 | 2 |
| #26013671 | 2 |
| #26013668 | 2 |
| #26013660 | 2 |
| #26013659 | 2 |
| C2×#19150223 | 2 |
| Q16×D349 | 2 |
| #26013647 | 2 |
| #137×C349 | 2 |
| #578 | 349 |