Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 95 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. #27212361 | C2 | semidirect |
| 2. #27212357 | C2 | semidirect |
| 3. #27212351 | C2 | semidirect |
| 4. #27212350 | C2 | semidirect |
| 5. #27212342 | C2 | semidirect |
| 7. #27212326 | C2 | semidirect |
| 8. C2×#20269750 | C2 | semidirect |
| 9. C22⋊Q8×C421 | C2 | semidirect |
| 66. C421 | #539 | semidirect |
| 73. C22⋊Q8 | D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27212361 | 2 |
| #27212357 | 2 |
| #27212351 | 2 |
| #27212350 | 2 |
| #27212342 | 2 |
| #27212340 | 2 |
| #27212326 | 2 |
| C2×#20269750 | 2 |
| C22⋊Q8×C421 | 2 |
| #539 | 421 |