Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
412 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. C22⋊C4×Dic271 | C2 | semidirect |
| 4. #31773664 | C2 | semidirect |
| 5. #342×C271 | C2 | semidirect |
| 8. C22×C4×D271 | C4 | semidirect |
| 11. C2×Dic271⋊C4 | C4 | semidirect |
| 13. C2×(C2×D271)⋊C4 | C4 | semidirect |
| 15. C2×C4×Dic271 | C4 | semidirect |
| 16. #22576074 | C4 | semidirect |
| 37. C22⋊Dic271 | C2×C4 | semidirect |
| 48. C22⋊C4×C271 | C2×C4 | semidirect |
| 53. C22×D271 | C42 | semidirect |
| 65. C2×Dic271 | C42 | semidirect |
| 109. Dic271 | #99 | semidirect |
| 118. C271 | C4×#99 | semidirect |
| 124. #342 | D271 | semidirect |
| 164. C22⋊C4 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C22⋊D271)⋊C4 | 2 |
| C2×#22576074 | 2 |
| C22⋊C4×Dic271 | 2 |
| #31773664 | 2 |
| #342×C271 | 2 |
| C4×#99 | 271 |