Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×#22576159 | C2 | semidirect |
| 3. #31774191 | C2 | semidirect |
| 4. #31774186 | C2 | semidirect |
| 5. #31774181 | C2 | semidirect |
| 6. #31774176 | C2 | semidirect |
| 7. #31773940 | C2 | semidirect |
| 8. #31773920 | C2 | semidirect |
| 11. #428×C271 | C2 | semidirect |
| 44. #16864654 | Q8 | semidirect |
| 87. Dic542 | C2×Q8 | semidirect |
| 89. D1084 | C2×Q8 | semidirect |
| 138. C271 | #3079 | semidirect |
| 147. #428 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576159 | 2 |
| #31774365 | 2 |
| #31774191 | 2 |
| #31774186 | 2 |
| #31774181 | 2 |
| #31774176 | 2 |
| #31773940 | 2 |
| #31773920 | 2 |
| #31773899 | 2 |
| #31773896 | 2 |
| #428×C271 | 2 |
| #3079 | 271 |