Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31774625 | C2 | semidirect |
| 3. #31774248 | C2 | semidirect |
| 4. #31774246 | C2 | semidirect |
| 5. #31774182 | C2 | semidirect |
| 6. #31774181 | C2 | semidirect |
| 9. C8×Dic542 | C2 | semidirect |
| 78. Dic542 | SD16 | semidirect |
| 118. C271 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774625 | 2 |
| D4×Dic542 | 2 |
| #31774248 | 2 |
| #31774246 | 2 |
| #31774182 | 2 |
| #31774181 | 2 |
| #31774102 | 2 |
| #31774100 | 2 |
| C8×Dic542 | 2 |
| #31773988 | 2 |
| C4×SD16×C271 | 2 |
| #3359 | 271 |