Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
836 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 169 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×#22576158 | C2 | semidirect |
| 3. C2×#22576149 | C2 | semidirect |
| 4. #31773812 | C2 | semidirect |
| 5. #31773802 | C2 | semidirect |
| 6. #31773798 | C2 | semidirect |
| 7. #31773768 | C2 | semidirect |
| 8. C4×C22⋊Dic271 | C2 | semidirect |
| 9. C2×C22⋊Q8×C271 | C2 | semidirect |
| 86. C2×Dic271 | #41 | semidirect |
| 136. C271 | #2432 | semidirect |
| 141. C2×C22⋊Q8 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864654 | 2 |
| C2×#22576158 | 2 |
| C2×#22576149 | 2 |
| #31773812 | 2 |
| #31773802 | 2 |
| #31773798 | 2 |
| #31773768 | 2 |
| C4×C22⋊Dic271 | 2 |
| C2×C22⋊Q8×C271 | 2 |
| #2432 | 271 |