Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#22576179 | C2 | semidirect |
| 2. #31774546 | C2 | semidirect |
| 3. #31774275 | C2 | semidirect |
| 4. #31774138 | C2 | semidirect |
| 5. #31774135 | C2 | semidirect |
| 6. #31774100 | C2 | semidirect |
| 7. #31774059 | C2 | semidirect |
| 8. #31774056 | C2 | semidirect |
| 9. D8×Dic271 | C2 | semidirect |
| 10. C8×C22⋊D271 | C2 | semidirect |
| 11. C2×#135×C271 | C2 | semidirect |
| 76. D8×C271 | D4 | semidirect |
| 129. Dic271 | #135 | semidirect |
| 136. C271 | #3283 | semidirect |
| 139. C2×#135 | D271 | semidirect |
| 198. D8 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576179 | 2 |
| #31774546 | 2 |
| #31774275 | 2 |
| #31774138 | 2 |
| #31774135 | 2 |
| #31774100 | 2 |
| #31774059 | 2 |
| #31774056 | 2 |
| D8×Dic271 | 2 |
| C8×C22⋊D271 | 2 |
| C2×#135×C271 | 2 |
| #3283 | 271 |