Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
158 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 158 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 |
|---|---|---|
| 1. C2×D349⋊C8 | C2 | semidirect |
| 2. #26013718 | C2 | semidirect |
| 3. #26013702 | C2 | semidirect |
| 4. #26013701 | C2 | semidirect |
| 12. #19150234 | C4 | semidirect |
| 14. #19150233 | C4 | semidirect |
| 16. #19150232 | C4 | semidirect |
| 22. #41×C349 | C4 | semidirect |
| 68. C349 | #416 | semidirect |
| 80. #41 | #13063703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D349⋊C8 | 2 |
| #26013718 | 2 |
| #26013702 | 2 |
| #26013701 | 2 |
| #41×D349 | 2 |
| #416 | 349 |