Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#22576191 | C2 | semidirect |
| 2. C2×#22576167 | C2 | semidirect |
| 4. #31774153 | C2 | semidirect |
| 5. #31774145 | C2 | semidirect |
| 6. #31774136 | C2 | semidirect |
| 7. #31774128 | C2 | semidirect |
| 8. #31773940 | C2 | semidirect |
| 9. #31773891 | C2 | semidirect |
| 10. C2×#22576084 | C2 | semidirect |
| 11. #536×C271 | C2 | semidirect |
| 54. #16864638 | D4 | semidirect |
| 143. C271 | #3063 | semidirect |
| 148. #536 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576191 | 2 |
| C2×#22576167 | 2 |
| #31774475 | 2 |
| #31774153 | 2 |
| #31774145 | 2 |
| #31774136 | 2 |
| #31774128 | 2 |
| #31773940 | 2 |
| #31773891 | 2 |
| C2×#22576084 | 2 |
| #536×C271 | 2 |
| #3063 | 271 |