Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
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×D421⋊C8 | C2 | semidirect |
| 2. #27212445 | C2 | semidirect |
| 3. #27212429 | C2 | semidirect |
| 4. #27212428 | C2 | semidirect |
| 12. #20269772 | C4 | semidirect |
| 14. #20269771 | C4 | semidirect |
| 16. #20269770 | C4 | semidirect |
| 22. #41×C421 | C4 | semidirect |
| 68. C421 | #416 | semidirect |
| 80. #41 | #13132997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D421⋊C8 | 2 |
| #27212445 | 2 |
| #27212429 | 2 |
| #27212428 | 2 |
| #41×D421 | 2 |
| #416 | 421 |