Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#19150232 | C2 | semidirect |
| 2. C2×#19150221 | C2 | semidirect |
| 3. #26013610 | C2 | semidirect |
| 4. #26013564 | C2 | semidirect |
| 5. #26013560 | C2 | semidirect |
| 6. #26013551 | C2 | semidirect |
| 7. C2×D8×C349 | C2 | semidirect |
| 25. Dic698 | D4 | semidirect |
| 40. D4×C349 | D4 | semidirect |
| 64. C349 | #449 | semidirect |
| 68. C2×D8 | D349 | semidirect |
| 98. D4 | C22⋊D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150232 | 2 |
| C2×#19150221 | 2 |
| #26013610 | 2 |
| #26013564 | 2 |
| #26013560 | 2 |
| #26013551 | 2 |
| C2×D8×C349 | 2 |
| #449 | 349 |