Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 3. #31773649 | C2 | semidirect |
| 4. Q8⋊(C271⋊C8) | C2 | semidirect |
| 6. #31773619 | C2 | semidirect |
| 7. #446×C271 | C2 | semidirect |
| 50. C271⋊C8 | M16 | semidirect |
| 77. C271 | #1592 | semidirect |
| 79. #446 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16864641 | 2 |
| #31773976 | 2 |
| #31773649 | 2 |
| Q8⋊(C271⋊C8) | 2 |
| #31773624 | 2 |
| #31773619 | 2 |
| #446×C271 | 2 |
| #1592 | 271 |