Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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. #27212356 | C2 | semidirect |
| 5. #27212346 | C2 | semidirect |
| 6. #27212345 | C2 | semidirect |
| 7. #27212331 | C2 | semidirect |
| 9. #27212325 | C2 | semidirect |
| 10. #27212324 | C2 | semidirect |
| 11. C2×C4⋊C4×C421 | C2 | semidirect |
| 72. C421 | #552 | semidirect |
| 84. C2×C4⋊C4 | 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 |
| #27212356 | 2 |
| #27212349 | 2 |
| #27212346 | 2 |
| #27212345 | 2 |
| #27212331 | 2 |
| C4×C22⋊D421 | 2 |
| #27212325 | 2 |
| #27212324 | 2 |
| C2×C4⋊C4×C421 | 2 |
| #552 | 421 |