Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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. #31774663 | C2 | semidirect |
| 3. #31773902 | C2 | semidirect |
| 4. #31773870 | C2 | semidirect |
| 5. #31773654 | C2 | semidirect |
| 6. #31773653 | C2 | semidirect |
| 7. #418×C271 | C2 | semidirect |
| 13. #22576156 | C4 | semidirect |
| 14. #22576147 | C4 | semidirect |
| 37. C2×C271⋊C8 | D4 | semidirect |
| 56. C2×C8×C271 | D4 | semidirect |
| 115. C271 | #1910 | semidirect |
| 120. #418 | D271 | semidirect |
| 165. C2×C8 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774663 | 2 |
| #31774464 | 2 |
| #31773902 | 2 |
| #31773870 | 2 |
| #31773654 | 2 |
| #31773653 | 2 |
| #418×C271 | 2 |
| #1910 | 271 |