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×#22576191 | C2 | semidirect |
| 2. C2×M16×D271 | C2 | semidirect |
| 4. C2×#22576136 | C2 | semidirect |
| 5. #31774154 | C2 | semidirect |
| 6. #31774146 | C2 | semidirect |
| 7. #31774137 | C2 | semidirect |
| 8. #31774129 | C2 | semidirect |
| 9. #31773940 | C2 | semidirect |
| 10. #31773899 | C2 | semidirect |
| 11. #419×C271 | C2 | semidirect |
| 15. C2×#16864644 | C22 | semidirect |
| 16. C2×#16864641 | C22 | semidirect |
| 36. #22576093 | C22 | semidirect |
| 37. #22576091 | C22 | semidirect |
| 38. #22576085 | C22 | semidirect |
| 39. #22576082 | C22 | semidirect |
| 43. #103×C271 | C22 | semidirect |
| 44. #103×C271 | C22 | semidirect |
| 64. #16864638 | D4 | semidirect |
| 145. C2×D271 | #137 | semidirect |
| 163. C271 | #3056 | semidirect |
| 174. #419 | D271 | semidirect |
| 206. #103 | C2×D271 | semidirect |
| 207. #103 | C2×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×M16×D271 | 2 |
| #31774409 | 2 |
| C2×#22576136 | 2 |
| #31774154 | 2 |
| #31774146 | 2 |
| #31774137 | 2 |
| #31774129 | 2 |
| #31773940 | 2 |
| #31773899 | 2 |
| #419×C271 | 2 |
| #3056 | 271 |