Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
386 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #31773758 | C2 | semidirect |
| 5. #31773758 | C2 | semidirect |
| 6. #31773663 | C2 | semidirect |
| 7. #342×C271 | C2 | semidirect |
| 11. #22576144 | C4 | semidirect |
| 40. C22×Dic271 | C2×C4 | semidirect |
| 62. C22⋊C4×C271 | C2×C4 | semidirect |
| 134. C271 | #1890 | semidirect |
| 142. #342 | D271 | semidirect |
| 196. 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×#22576144 | 2 |
| #31774370 | 2 |
| C2×#22576074 | 2 |
| #31773758 | 2 |
| #31773663 | 2 |
| #342×C271 | 2 |
| #1890 | 271 |