Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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. #31774305 | C2 | semidirect |
| 3. #31774297 | C2 | semidirect |
| 4. #31774294 | C2 | semidirect |
| 30. #16864638 | Q8 | semidirect |
| 41. C2×C8×C271 | Q8 | semidirect |
| 75. C271 | #3163 | semidirect |
| 109. C2×C8 | Dic542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774525 | 2 |
| #31774305 | 2 |
| #31774297 | 2 |
| #31774294 | 2 |
| #31773940 | 2 |
| C2×#22576092 | 2 |
| #31773852 | 2 |
| #427×C271 | 2 |
| #3163 | 271 |