Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. #31773951 | C2 | semidirect |
| 3. #31773947 | C2 | semidirect |
| 4. #31773920 | C2 | semidirect |
| 6. M16×Dic271 | C2 | semidirect |
| 17. Dic271⋊C8 | C22 | semidirect |
| 19. #22576070 | C22 | semidirect |
| 20. C8×Dic271 | C22 | semidirect |
| 56. C2×Dic271 | M16 | semidirect |
| 92. C271 | #2920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic271 | 2 |
| #31773951 | 2 |
| #31773947 | 2 |
| #31773920 | 2 |
| #31773861 | 2 |
| M16×Dic271 | 2 |
| #407×C271 | 2 |
| #2920 | 271 |