Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22576183 | C2 | semidirect |
| 2. C22×C8×D271 | C2 | semidirect |
| 3. #31774410 | C2 | semidirect |
| 4. #31774135 | C2 | semidirect |
| 5. #31774134 | C2 | semidirect |
| 6. #31774133 | C2 | semidirect |
| 7. #31774129 | C2 | semidirect |
| 8. #31774128 | C2 | semidirect |
| 9. #31773934 | C2 | semidirect |
| 10. #31773892 | C2 | semidirect |
| 11. #467×C271 | C2 | semidirect |
| 15. C2×#16864641 | C22 | semidirect |
| 16. C2×D2168 | C22 | semidirect |
| 31. #22576094 | C22 | semidirect |
| 32. #22576091 | C22 | semidirect |
| 33. #22576084 | C22 | semidirect |
| 34. #22576082 | C22 | semidirect |
| 35. #22576080 | C22 | semidirect |
| 36. C2×Q16×C271 | C22 | semidirect |
| 39. #107×C271 | C22 | semidirect |
| 40. #103×C271 | C22 | semidirect |
| 64. C8×D271 | D4 | semidirect |
| 118. C22×C271 | #135 | semidirect |
| 129. C2×D271 | #135 | semidirect |
| 145. C271 | #3050 | semidirect |
| 151. #467 | D271 | semidirect |
| 161. C2×Q16 | C2×D271 | semidirect |
| 181. #107 | C2×D271 | semidirect |
| 184. #103 | C2×D271 | semidirect |
| 274. C22 | #22576183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576183 | 2 |
| C22×C8×D271 | 2 |
| #31774410 | 2 |
| #31774135 | 2 |
| #31774134 | 2 |
| #31774133 | 2 |
| #31774129 | 2 |
| #31774128 | 2 |
| #31773934 | 2 |
| #31773892 | 2 |
| #467×C271 | 2 |
| #3050 | 271 |