Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 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. #31774183 | C2 | semidirect |
| 4. C8×Dic542 | C2 | semidirect |
| 5. #31773642 | C2 | semidirect |
| 7. #334×C271 | C2 | semidirect |
| 46. Dic542 | SD16 | semidirect |
| 62. C8×C271 | SD16 | semidirect |
| 79. C271 | #1666 | semidirect |
| 85. #334 | D271 | semidirect |
| 142. C8 | #16864643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774270 | 2 |
| #31774183 | 2 |
| #31774098 | 2 |
| C8×Dic542 | 2 |
| #31773642 | 2 |
| #31773640 | 2 |
| #334×C271 | 2 |
| #1666 | 271 |