Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 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 |
|---|---|---|
| 2. C4⋊Q8×D271 | C2 | semidirect |
| 4. #31774107 | C2 | semidirect |
| 5. #31774105 | C2 | semidirect |
| 6. #31774103 | C2 | semidirect |
| 7. #31774101 | C2 | semidirect |
| 8. #31774099 | C2 | semidirect |
| 9. #31773919 | C2 | semidirect |
| 10. #31773904 | C2 | semidirect |
| 11. #462×C271 | C2 | semidirect |
| 132. C4×C271 | #137 | semidirect |
| 139. Dic271 | #137 | semidirect |
| 145. C271 | #3039 | semidirect |
| 152. #462 | D271 | semidirect |
| 283. C4 | #22576192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576192 | 2 |
| C4⋊Q8×D271 | 2 |
| C4×#16864655 | 2 |
| #31774107 | 2 |
| #31774105 | 2 |
| #31774103 | 2 |
| #31774101 | 2 |
| #31774099 | 2 |
| #31773919 | 2 |
| #31773904 | 2 |
| #462×C271 | 2 |
| #3039 | 271 |