Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31774612 | C2 | semidirect |
| 2. #31774552 | C2 | semidirect |
| 3. #31774295 | C2 | semidirect |
| 4. #31774220 | C2 | semidirect |
| 5. #31774214 | C2 | semidirect |
| 6. #31774187 | C2 | semidirect |
| 7. #31774177 | C2 | semidirect |
| 8. #31774147 | C2 | semidirect |
| 9. #31773976 | C2 | semidirect |
| 10. #31773938 | C2 | semidirect |
| 11. C4×D8×C271 | C2 | semidirect |
| 101. C8×C271 | #41 | semidirect |
| 127. C271 | #3354 | semidirect |
| 137. 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 |
|---|---|
| #31774612 | 2 |
| #31774552 | 2 |
| #31774295 | 2 |
| #31774220 | 2 |
| #31774214 | 2 |
| #31774187 | 2 |
| #31774177 | 2 |
| #31774147 | 2 |
| #31773976 | 2 |
| #31773938 | 2 |
| C4×D8×C271 | 2 |
| #3354 | 271 |