Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 153 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. C22×Q8×D271 | C2 | semidirect |
| 2. C2×#22576193 | C2 | semidirect |
| 3. C2×#22576191 | C2 | semidirect |
| 5. #31774054 | C2 | semidirect |
| 6. #31774037 | C2 | semidirect |
| 7. #31773905 | C2 | semidirect |
| 8. #31773860 | C2 | semidirect |
| 9. #419×C271 | C2 | semidirect |
| 21. C2×Dic1084 | C22 | semidirect |
| 22. C2×#16864644 | C22 | semidirect |
| 23. C2×#16864643 | C22 | semidirect |
| 24. C2×#16864641 | C22 | semidirect |
| 31. #22576083 | C22 | semidirect |
| 36. #103×C271 | C22 | semidirect |
| 44. C2×Dic542 | D4 | semidirect |
| 73. C2×Q8×C271 | D4 | semidirect |
| 127. C2×D271 | #137 | semidirect |
| 141. C271 | #3004 | semidirect |
| 150. #419 | D271 | semidirect |
| 177. #103 | C2×D271 | semidirect |
| 194. C2×Q8 | D1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D271 | 2 |
| C2×#22576193 | 2 |
| C2×#22576191 | 2 |
| #31774409 | 2 |
| #31774054 | 2 |
| #31774037 | 2 |
| #31773905 | 2 |
| #31773860 | 2 |
| #419×C271 | 2 |
| #3004 | 271 |