Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
106 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 41 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. #31774329 | C2 | semidirect |
| 2. #31773737 | C2 | semidirect |
| 3. #31773735 | C2 | semidirect |
| 4. #31773734 | C2 | semidirect |
| 5. #31773732 | C2 | semidirect |
| 6. C2×C271⋊C32 | C2 | semidirect |
| 7. #508×C271 | C2 | semidirect |
| 52. C271 | #2262 | semidirect |
| 55. #508 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774329 | 2 |
| #31773737 | 2 |
| #31773735 | 2 |
| #31773734 | 2 |
| #31773732 | 2 |
| C2×C271⋊C32 | 2 |
| #508×C271 | 2 |
| #2262 | 271 |