Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
484 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 177 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. #31773801 | C2 | semidirect |
| 5. #31773780 | C2 | semidirect |
| 6. #31773779 | C2 | semidirect |
| 7. #31773748 | C2 | semidirect |
| 11. #22576139 | C4 | semidirect |
| 115. C271 | #2332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576139 | 2 |
| #31773801 | 2 |
| #31773791 | 2 |
| #31773785 | 2 |
| #31773780 | 2 |
| #31773779 | 2 |
| #31773748 | 2 |
| C4×C22⋊Dic271 | 2 |
| #381×C271 | 2 |
| #2332 | 271 |