Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
936 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 277 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. C22×C4×Dic271 | C2 | semidirect |
| 3. #31773802 | C2 | semidirect |
| 4. #31773798 | C2 | semidirect |
| 5. #31773774 | C2 | semidirect |
| 6. C4×(C2×D271)⋊C4 | C2 | semidirect |
| 7. C2×#117×C271 | C2 | semidirect |
| 10. C2×#16864654 | C4 | semidirect |
| 30. C2×Dic542 | C2×C4 | semidirect |
| 33. C2×D1084 | C2×C4 | semidirect |
| 43. C2×C4×D271 | C2×C4 | semidirect |
| 70. C2×Dic271 | #41 | semidirect |
| 79. C2×C4×C271 | C22⋊C4 | semidirect |
| 109. C271 | #2297 | semidirect |
| 112. C2×#117 | D271 | semidirect |
| 189. C2×C4 | (C2×D271)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864654 | 2 |
| C22×C4×Dic271 | 2 |
| #31773802 | 2 |
| #31773798 | 2 |
| #31773774 | 2 |
| C4×(C2×D271)⋊C4 | 2 |
| C2×#117×C271 | 2 |
| #2297 | 271 |