Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×#22576086 | C2 | semidirect |
| 3. #31773899 | C2 | semidirect |
| 4. #31773766 | C2 | semidirect |
| 5. #343×C271 | C2 | semidirect |
| 34. C4×Dic271 | D4 | semidirect |
| 85. C271 | #2039 | semidirect |
| 91. #343 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774478 | 2 |
| C2×#22576086 | 2 |
| #31773899 | 2 |
| #31773766 | 2 |
| #343×C271 | 2 |
| #2039 | 271 |