Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
242 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 103 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. #27212346 | C2 | semidirect |
| 2. #27212345 | C2 | semidirect |
| 3. #27212344 | C2 | semidirect |
| 4. #27212344 | C2 | semidirect |
| 5. #27212343 | C2 | semidirect |
| 6. #27212342 | C2 | semidirect |
| 9. C22⋊Q8×C421 | C2 | semidirect |
| 11. C2×Dic842 | C22 | semidirect |
| 12. C2×Dic842 | C22 | semidirect |
| 16. C4⋊Dic421 | C22 | semidirect |
| 17. C4⋊Dic421 | C22 | semidirect |
| 18. #20269750 | C22 | semidirect |
| 19. #20269750 | C22 | semidirect |
| 20. #20269750 | C22 | semidirect |
| 26. C2×Q8×C421 | C22 | semidirect |
| 28. C4⋊C4×C421 | C22 | semidirect |
| 29. C4⋊C4×C421 | C22 | semidirect |
| 33. C22×D421 | Q8 | semidirect |
| 70. C421 | #543 | semidirect |
| 78. C22⋊Q8 | D421 | semidirect |
| 84. C2×Q8 | C2×D421 | semidirect |
| 94. C4⋊C4 | C2×D421 | semidirect |
| 95. C4⋊C4 | C2×D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27212346 | 2 |
| #27212345 | 2 |
| #27212344 | 2 |
| #27212343 | 2 |
| #27212342 | 2 |
| C2×#20269748 | 2 |
| C22⋊C4×D421 | 2 |
| C22⋊Q8×C421 | 2 |
| #543 | 421 |