Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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×#22576190 | C2 | semidirect |
| 2. C2×M16×D271 | C2 | semidirect |
| 4. C2×#22576140 | C2 | semidirect |
| 5. #31774154 | C2 | semidirect |
| 6. #31774142 | C2 | semidirect |
| 7. #31774137 | C2 | semidirect |
| 8. #31774125 | C2 | semidirect |
| 9. #31773937 | C2 | semidirect |
| 10. #31773907 | C2 | semidirect |
| 11. #417×C271 | C2 | semidirect |
| 15. C2×#16864644 | C22 | semidirect |
| 16. C2×#16864642 | C22 | semidirect |
| 36. #22576093 | C22 | semidirect |
| 37. #22576091 | C22 | semidirect |
| 38. #22576085 | C22 | semidirect |
| 39. #22576085 | C22 | semidirect |
| 43. #103×C271 | C22 | semidirect |
| 44. #102×C271 | C22 | semidirect |
| 62. #16864638 | D4 | semidirect |
| 145. C2×D271 | #137 | semidirect |
| 163. C271 | #3056 | semidirect |
| 175. #417 | D271 | semidirect |
| 207. #103 | C2×D271 | semidirect |
| 208. #102 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576190 | 2 |
| C2×M16×D271 | 2 |
| #31774404 | 2 |
| C2×#22576140 | 2 |
| #31774154 | 2 |
| #31774142 | 2 |
| #31774137 | 2 |
| #31774125 | 2 |
| #31773937 | 2 |
| #31773907 | 2 |
| #417×C271 | 2 |
| #3056 | 271 |