Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 185 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. #31773785 | C2 | semidirect |
| 4. #31773785 | C2 | semidirect |
| 5. #31773784 | C2 | semidirect |
| 6. #31773748 | C2 | semidirect |
| 7. C22⋊C4×Dic271 | C2 | semidirect |
| 8. C4×C22⋊Dic271 | C2 | semidirect |
| 11. #22576141 | C4 | semidirect |
| 34. C22×Dic271 | C2×C4 | semidirect |
| 41. Dic271⋊C4 | C2×C4 | semidirect |
| 45. C22⋊Dic271 | C2×C4 | semidirect |
| 126. C271 | #2374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576141 | 2 |
| #31773800 | 2 |
| #31773785 | 2 |
| #31773784 | 2 |
| #31773748 | 2 |
| C22⋊C4×Dic271 | 2 |
| C4×C22⋊Dic271 | 2 |
| #386×C271 | 2 |
| #2374 | 271 |