Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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. #31774189 | C2 | semidirect |
| 3. #31774184 | C2 | semidirect |
| 4. #31774179 | C2 | semidirect |
| 5. #31774174 | C2 | semidirect |
| 6. #31773937 | C2 | semidirect |
| 7. #31773921 | C2 | semidirect |
| 9. C2×C4⋊Q8×C271 | C2 | semidirect |
| 36. #16864654 | Q8 | semidirect |
| 72. Dic542 | C2×Q8 | semidirect |
| 74. D1084 | C2×Q8 | semidirect |
| 121. C271 | #3079 | semidirect |
| 123. C2×C4⋊Q8 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16864654 | 2 |
| #31774189 | 2 |
| #31774184 | 2 |
| #31774179 | 2 |
| #31774174 | 2 |
| #31773937 | 2 |
| #31773921 | 2 |
| #31773896 | 2 |
| C2×C4⋊Q8×C271 | 2 |
| #3079 | 271 |