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. #31774233 | C2 | semidirect |
| 5. #31774206 | C2 | semidirect |
| 6. #31774117 | C2 | semidirect |
| 7. #31774053 | C2 | semidirect |
| 8. #31774001 | C2 | semidirect |
| 9. #31773998 | C2 | semidirect |
| 10. #31773951 | C2 | semidirect |
| 131. C271 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774428 | 2 |
| C2×Q8×Dic271 | 2 |
| #31774233 | 2 |
| #31774213 | 2 |
| #31774206 | 2 |
| #31774117 | 2 |
| #31774053 | 2 |
| #31774001 | 2 |
| #31773998 | 2 |
| #31773951 | 2 |
| #448×C271 | 2 |
| #3117 | 271 |