Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D271 | C2 | semidirect |
| 3. #31774191 | C2 | semidirect |
| 4. #31774185 | C2 | semidirect |
| 5. #31774183 | C2 | semidirect |
| 6. #31774179 | C2 | semidirect |
| 7. #31774177 | C2 | semidirect |
| 8. #31773938 | C2 | semidirect |
| 9. #31773919 | C2 | semidirect |
| 11. #474×C271 | C2 | semidirect |
| 44. #16864653 | Q8 | semidirect |
| 86. Dic542 | C2×Q8 | semidirect |
| 105. D4×C271 | C2×Q8 | semidirect |
| 137. C271 | #3079 | semidirect |
| 146. #474 | D271 | semidirect |
| 229. D4 | Q8×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D271 | 2 |
| C4×#16864653 | 2 |
| #31774191 | 2 |
| #31774185 | 2 |
| #31774183 | 2 |
| #31774179 | 2 |
| #31774177 | 2 |
| #31773938 | 2 |
| #31773919 | 2 |
| #31773895 | 2 |
| #474×C271 | 2 |
| #3079 | 271 |