Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
408 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 408 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. #31774447 | C2 | semidirect |
| 2. #31774431 | C2 | semidirect |
| 3. #31774306 | C2 | semidirect |
| 4. #31774286 | C2 | semidirect |
| 5. #31774262 | C2 | semidirect |
| 6. #31774257 | C2 | semidirect |
| 7. #31774150 | C2 | semidirect |
| 8. #31774143 | C2 | semidirect |
| 9. C4×#16864643 | C2 | semidirect |
| 10. C4×D2168 | C2 | semidirect |
| 11. C4×M16×C271 | C2 | semidirect |
| 110. C8×C271 | #41 | semidirect |
| 137. C271 | #3171 | semidirect |
| 149. C4×M16 | D271 | semidirect |
| 248. C8 | #16864654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774447 | 2 |
| #31774431 | 2 |
| #31774306 | 2 |
| #31774286 | 2 |
| #31774262 | 2 |
| #31774257 | 2 |
| #31774150 | 2 |
| #31774143 | 2 |
| C4×#16864643 | 2 |
| C4×D2168 | 2 |
| C4×M16×C271 | 2 |
| #3171 | 271 |