Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
190 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 190 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. D421⋊M16 | C2 | semidirect |
| 2. #27212445 | C2 | semidirect |
| 3. #27212428 | C2 | semidirect |
| 7. D421⋊C8 | C22 | semidirect |
| 8. C4⋊#13132997 | C22 | semidirect |
| 12. C2×D1684 | C4 | semidirect |
| 16. D4×D421 | C4 | semidirect |
| 19. C2×D4×C421 | C4 | semidirect |
| 61. C421 | #418 | semidirect |
| 74. C2×D4 | #13132997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D421⋊M16 | 2 |
| #27212445 | 2 |
| #27212428 | 2 |
| C2×D4×D421 | 2 |
| #418 | 421 |