Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
334 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 97 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. #31773906 | C2 | semidirect |
| 4. #31773804 | C2 | semidirect |
| 5. #31773665 | C2 | semidirect |
| 6. #31773658 | C2 | semidirect |
| 24. #137×C271 | C4 | semidirect |
| 54. C2×Q8×C271 | C2×C4 | semidirect |
| 64. M16×C271 | C2×C4 | semidirect |
| 124. C271 | #1882 | semidirect |
| 136. #137 | Dic271 | semidirect |
| 162. C2×Q8 | C2×Dic271 | semidirect |
| 177. M16 | C2×Dic271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774380 | 2 |
| C2×#22576087 | 2 |
| #31773906 | 2 |
| #31773804 | 2 |
| #31773665 | 2 |
| #31773658 | 2 |
| C2×#137×C271 | 2 |
| #1882 | 271 |