Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #31774097 | C2 | semidirect |
| 3. Q8×C271⋊C8 | C2 | semidirect |
| 4. #31773649 | C2 | semidirect |
| 5. #31773641 | C2 | semidirect |
| 6. #31773640 | C2 | semidirect |
| 7. #460×C271 | C2 | semidirect |
| 52. C271⋊C8 | SD16 | semidirect |
| 55. Q8×C271 | D8 | semidirect |
| 86. C271 | #1668 | semidirect |
| 90. #460 | D271 | semidirect |
| 133. Q8 | #16864639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774273 | 2 |
| #31774097 | 2 |
| Q8×C271⋊C8 | 2 |
| #31773649 | 2 |
| #31773641 | 2 |
| #31773640 | 2 |
| #460×C271 | 2 |
| #1668 | 271 |