Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
456 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 145 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. #31774447 | C2 | semidirect |
| 2. #31774300 | C2 | semidirect |
| 3. #31774273 | C2 | semidirect |
| 4. #31774245 | C2 | semidirect |
| 5. #31774243 | C2 | semidirect |
| 6. #31774131 | C2 | semidirect |
| 7. C4×#16864639 | C2 | semidirect |
| 8. C2×C4×C271⋊C8 | C2 | semidirect |
| 9. #532×C271 | C2 | semidirect |
| 77. C271⋊C8 | #41 | semidirect |
| 89. C2×C4×C271 | D8 | semidirect |
| 120. C271 | #3169 | semidirect |
| 123. #532 | D271 | semidirect |
| 208. C2×C4 | #16864639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774447 | 2 |
| #31774300 | 2 |
| #31774273 | 2 |
| #31774245 | 2 |
| #31774243 | 2 |
| #31774131 | 2 |
| C4×#16864639 | 2 |
| C2×C4×C271⋊C8 | 2 |
| #532×C271 | 2 |
| #3169 | 271 |