Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 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. #31774307 | C2 | semidirect |
| 3. #31774296 | C2 | semidirect |
| 24. #16864638 | Q8 | semidirect |
| 65. C271 | #3166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774454 | 2 |
| #31774307 | 2 |
| #31774296 | 2 |
| #31773937 | 2 |
| C4×#16864638 | 2 |
| C2×#125×C271 | 2 |
| #3166 | 271 |