Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 131 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. #31774203 | C2 | semidirect |
| 4. #31774202 | C2 | semidirect |
| 5. #31774189 | C2 | semidirect |
| 6. #31774183 | C2 | semidirect |
| 7. #31774182 | C2 | semidirect |
| 11. #477×C271 | C2 | semidirect |
| 47. Q8×D271 | Q8 | semidirect |
| 130. C271 | #3078 | semidirect |
| 137. #477 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774452 | 2 |
| C4×Q8×D271 | 2 |
| #31774203 | 2 |
| #31774202 | 2 |
| #31774189 | 2 |
| #31774183 | 2 |
| #31774182 | 2 |
| #31773938 | 2 |
| #31773919 | 2 |
| #31773904 | 2 |
| #477×C271 | 2 |
| #3078 | 271 |