Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
456 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 149 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. #31774302 | C2 | semidirect |
| 3. #31774274 | C2 | semidirect |
| 4. #31774244 | C2 | semidirect |
| 5. #31774133 | C2 | semidirect |
| 6. C4×D2168 | C2 | semidirect |
| 7. C2×C4×C8×C271 | C2 | semidirect |
| 57. C2×C4×C271 | D8 | semidirect |
| 65. C8×C271 | #41 | semidirect |
| 85. C271 | #3169 | semidirect |
| 93. C2×C4×C8 | D271 | semidirect |
| 143. C2×C4 | D2168 | semidirect |
| 151. C8 | #16864654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774447 | 2 |
| #31774302 | 2 |
| #31774274 | 2 |
| #31774244 | 2 |
| #31774133 | 2 |
| C4×D2168 | 2 |
| C2×C4×C8×C271 | 2 |
| #3169 | 271 |