Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #31774697 | C2 | semidirect |
| 2. C2×#22576186 | C2 | semidirect |
| 3. #31774464 | C2 | semidirect |
| 4. #31773915 | C2 | semidirect |
| 5. #31773870 | C2 | semidirect |
| 6. #31773668 | C2 | semidirect |
| 7. #418×C271 | C2 | semidirect |
| 40. C2×Dic542 | D4 | semidirect |
| 42. C2×D1084 | D4 | semidirect |
| 55. #16864638 | D4 | semidirect |
| 71. C2×C8×C271 | D4 | semidirect |
| 142. C271 | #2008 | semidirect |
| 148. #418 | D271 | semidirect |
| 210. C2×C8 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774697 | 2 |
| C2×#22576186 | 2 |
| #31774464 | 2 |
| #31773915 | 2 |
| #31773870 | 2 |
| #31773668 | 2 |
| #418×C271 | 2 |
| #2008 | 271 |