Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
552 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 1. C2×#22576189 | C2 | semidirect |
| 3. C4⋊Q8×D271 | C2 | semidirect |
| 4. #31774288 | C2 | semidirect |
| 5. #31774277 | C2 | semidirect |
| 6. #31774276 | C2 | semidirect |
| 7. #31774269 | C2 | semidirect |
| 8. C4×#16864637 | C2 | semidirect |
| 9. #492×C271 | C2 | semidirect |
| 45. #16864637 | D4 | semidirect |
| 88. C4×C271 | #137 | semidirect |
| 98. C271 | #3152 | semidirect |
| 107. #492 | D271 | semidirect |
| 191. C4 | #22576189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576189 | 2 |
| #31774445 | 2 |
| C4⋊Q8×D271 | 2 |
| #31774288 | 2 |
| #31774277 | 2 |
| #31774276 | 2 |
| #31774269 | 2 |
| C4×#16864637 | 2 |
| #492×C271 | 2 |
| #3152 | 271 |