Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 123 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×Q8×Dic271 | C2 | semidirect |
| 3. #31774211 | C2 | semidirect |
| 4. #31774208 | C2 | semidirect |
| 5. #31774190 | C2 | semidirect |
| 6. #31774095 | C2 | semidirect |
| 7. #31774036 | C2 | semidirect |
| 8. #31774000 | C2 | semidirect |
| 9. #31773998 | C2 | semidirect |
| 10. #31773951 | C2 | semidirect |
| 11. #448×C271 | C2 | semidirect |
| 104. Q8×C271 | #41 | semidirect |
| 140. C271 | #3112 | semidirect |
| 149. #448 | D271 | semidirect |
| 229. Q8 | #16864653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774442 | 2 |
| C2×Q8×Dic271 | 2 |
| #31774211 | 2 |
| #31774208 | 2 |
| #31774190 | 2 |
| #31774095 | 2 |
| #31774036 | 2 |
| #31774000 | 2 |
| #31773998 | 2 |
| #31773951 | 2 |
| #448×C271 | 2 |
| #3112 | 271 |