Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
484 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
| 3. C2×Q8×Dic271 | C2 | semidirect |
| 4. #31774121 | C2 | semidirect |
| 5. #31774117 | C2 | semidirect |
| 6. #31774105 | C2 | semidirect |
| 7. #31774095 | C2 | semidirect |
| 8. #31773920 | C2 | semidirect |
| 9. #31773899 | C2 | semidirect |
| 10. #31773898 | C2 | semidirect |
| 11. C2×#137×C271 | C2 | semidirect |
| 80. C2×Q8×C271 | D4 | semidirect |
| 150. Dic271 | #137 | semidirect |
| 157. C271 | #3037 | semidirect |
| 160. C2×#137 | D271 | semidirect |
| 210. C2×Q8 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576191 | 2 |
| #31774443 | 2 |
| C2×Q8×Dic271 | 2 |
| #31774121 | 2 |
| #31774117 | 2 |
| #31774105 | 2 |
| #31774095 | 2 |
| #31773920 | 2 |
| #31773899 | 2 |
| #31773898 | 2 |
| C2×#137×C271 | 2 |
| #3037 | 271 |