Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
166 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 166 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 |
|---|---|---|
| 1. #31774021 | C2 | semidirect |
| 4. #31773647 | C2 | semidirect |
| 5. #31773629 | C2 | semidirect |
| 6. #31773619 | C2 | semidirect |
| 42. Dic542 | M16 | semidirect |
| 49. C271⋊C8 | SD16 | semidirect |
| 77. C271 | #1583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774021 | 2 |
| C4×#16864642 | 2 |
| #31773975 | 2 |
| #31773647 | 2 |
| #31773629 | 2 |
| #31773619 | 2 |
| D4⋊C8×C271 | 2 |
| #1583 | 271 |