Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31774444 | C2 | semidirect |
| 2. #31774301 | C2 | semidirect |
| 3. #31774272 | C2 | semidirect |
| 4. #31774242 | C2 | semidirect |
| 5. #31774134 | C2 | semidirect |
| 6. #31774132 | C2 | semidirect |
| 7. #31774130 | C2 | semidirect |
| 8. C4×D2168 | C2 | semidirect |
| 9. C4×#16864639 | C2 | semidirect |
| 10. C4×C8×D271 | C2 | semidirect |
| 11. C4×D8×C271 | C2 | semidirect |
| 89. C4×D271 | D8 | semidirect |
| 91. C271⋊C8 | #41 | semidirect |
| 101. C8×C271 | #41 | semidirect |
| 127. C271 | #3169 | semidirect |
| 138. C4×D8 | D271 | semidirect |
| 229. C8 | #16864654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774444 | 2 |
| #31774301 | 2 |
| #31774272 | 2 |
| #31774242 | 2 |
| #31774134 | 2 |
| #31774132 | 2 |
| #31774130 | 2 |
| C4×D2168 | 2 |
| C4×#16864639 | 2 |
| C4×C8×D271 | 2 |
| C4×D8×C271 | 2 |
| #3169 | 271 |