Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 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. C2×#22576179 | C2 | semidirect |
| 2. #31774567 | C2 | semidirect |
| 3. #31774130 | C2 | semidirect |
| 4. #31774094 | C2 | semidirect |
| 5. #31774039 | C2 | semidirect |
| 6. C4×Dic1084 | C2 | semidirect |
| 7. C8×D1084 | C2 | semidirect |
| 8. #493×C271 | C2 | semidirect |
| 37. Dic1084 | D4 | semidirect |
| 86. C4×C271 | #135 | semidirect |
| 97. C271 | #3287 | semidirect |
| 101. #493 | D271 | semidirect |
| 187. C4 | #22576179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576179 | 2 |
| #31774567 | 2 |
| #31774130 | 2 |
| #31774094 | 2 |
| #31774039 | 2 |
| C4×Dic1084 | 2 |
| C8×D1084 | 2 |
| #493×C271 | 2 |
| #3287 | 271 |