Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 2. #31774379 | C2 | semidirect |
| 3. #31774010 | C2 | semidirect |
| 4. #31774008 | C2 | semidirect |
| 5. #31774004 | C2 | semidirect |
| 6. C4×#16864641 | C2 | semidirect |
| 7. #31773982 | C2 | semidirect |
| 8. #106×D271 | C2 | semidirect |
| 9. #31773897 | C2 | semidirect |
| 10. #31773854 | C2 | semidirect |
| 11. #441×C271 | C2 | semidirect |
| 13. #22576183 | C4 | semidirect |
| 41. #16864655 | C2×C4 | semidirect |
| 49. #16864641 | C2×C4 | semidirect |
| 50. D2168 | C2×C4 | semidirect |
| 54. C8×D271 | C2×C4 | semidirect |
| 65. Q16×C271 | C2×C4 | semidirect |
| 114. C271 | #2952 | semidirect |
| 121. #441 | D271 | semidirect |
| 165. Q16 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576183 | 2 |
| #31774379 | 2 |
| #31774010 | 2 |
| #31774008 | 2 |
| #31774004 | 2 |
| C4×#16864641 | 2 |
| #31773982 | 2 |
| #106×D271 | 2 |
| #31773897 | 2 |
| #31773854 | 2 |
| #441×C271 | 2 |
| #2952 | 271 |