Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
104 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 39 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. #26013669 | C2 | semidirect |
| 3. C2×#19150222 | C2 | semidirect |
| 4. #26013575 | C2 | semidirect |
| 5. #26013557 | C2 | semidirect |
| 6. #26013555 | C2 | semidirect |
| 7. #131×C349 | C2 | semidirect |
| 51. C349 | #471 | semidirect |
| 56. #131 | D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26013669 | 2 |
| #26013664 | 2 |
| C2×#19150222 | 2 |
| #26013575 | 2 |
| #26013557 | 2 |
| #26013555 | 2 |
| #131×C349 | 2 |
| #471 | 349 |