Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
266 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 140 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. #27212453 | C2 | direct (N × H) |
| 2. C2×#20269781 | C2 | semidirect |
| 3. C2×#20269780 | C2 | semidirect |
| 4. C2×D421⋊C8 | C2 | semidirect |
| 5. C22×#16809897 | C2 | semidirect |
| 7. #20269781 | C22 | semidirect |
| 8. #20269780 | C22 | semidirect |
| 9. D421⋊C8 | C22 | semidirect |
| 13. C2×#16809897 | C22 | semidirect |
| 46. C2×C421 | #131 | semidirect |
| 49. C421 | C2×#131 | semidirect |
| 97. C2 | #27212453 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27212453 | 2 |
| C2×#20269781 | 2 |
| C2×#20269780 | 2 |
| C2×D421⋊C8 | 2 |
| C22×#16809897 | 2 |
| C2×#20269770 | 2 |
| C2×#131 | 421 |