Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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×#22576082 | C2 | semidirect |
| 3. C2×#22576080 | C2 | semidirect |
| 4. C2×(C2×D271)⋊C8 | C2 | semidirect |
| 5. #31773754 | C2 | semidirect |
| 6. #31773659 | C2 | semidirect |
| 7. C2×#107×C271 | C2 | semidirect |
| 56. C2×C8×C271 | D4 | semidirect |
| 143. C271 | #2033 | semidirect |
| 146. C2×#107 | D271 | semidirect |
| 196. C2×C8 | D1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576135 | 2 |
| C2×#22576082 | 2 |
| C2×#22576080 | 2 |
| C2×(C2×D271)⋊C8 | 2 |
| #31773754 | 2 |
| #31773659 | 2 |
| C2×#107×C271 | 2 |
| #2033 | 271 |