Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 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. #31773804 | C2 | semidirect |
| 3. #31773789 | C2 | semidirect |
| 4. #31773787 | C2 | semidirect |
| 6. C4×(C2×D271)⋊C4 | C2 | semidirect |
| 7. #31773744 | C2 | semidirect |
| 8. #31773742 | C2 | semidirect |
| 9. #391×C271 | C2 | semidirect |
| 12. #22576149 | C4 | semidirect |
| 46. (C2×D271)⋊C4 | C2×C4 | semidirect |
| 47. (C2×D271)⋊C4 | C2×C4 | semidirect |
| 51. C4×Dic271 | C2×C4 | semidirect |
| 54. C2×Q8×C271 | C2×C4 | semidirect |
| 123. C271 | #2372 | semidirect |
| 127. #391 | D271 | semidirect |
| 159. C2×Q8 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576149 | 2 |
| #31773804 | 2 |
| #31773789 | 2 |
| #31773787 | 2 |
| #31773775 | 2 |
| C4×(C2×D271)⋊C4 | 2 |
| #31773744 | 2 |
| #31773742 | 2 |
| #391×C271 | 2 |
| #2372 | 271 |