Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31774230 | C2 | semidirect |
| 5. #31774202 | C2 | semidirect |
| 6. #31774121 | C2 | semidirect |
| 8. #31774004 | C2 | semidirect |
| 9. #31774000 | C2 | semidirect |
| 10. #31773951 | C2 | semidirect |
| 11. #451×C271 | C2 | semidirect |
| 131. C271 | #3117 | semidirect |
| 139. #451 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774433 | 2 |
| C2×Q8×Dic271 | 2 |
| #31774230 | 2 |
| #31774216 | 2 |
| #31774202 | 2 |
| #31774121 | 2 |
| #31774036 | 2 |
| #31774004 | 2 |
| #31774000 | 2 |
| #31773951 | 2 |
| #451×C271 | 2 |
| #3117 | 271 |