Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#22576071 | C2 | semidirect |
| 3. #31773638 | C2 | semidirect |
| 4. #31773636 | C2 | semidirect |
| 5. #432×C271 | C2 | semidirect |
| 90. C271 | #1532 | semidirect |
| 93. #432 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774431 | 2 |
| C2×#22576071 | 2 |
| #31773638 | 2 |
| #31773636 | 2 |
| #432×C271 | 2 |
| #1532 | 271 |