Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
754 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. C2×#22576192 | C2 | semidirect |
| 3. C22⋊Q8×D271 | C2 | semidirect |
| 4. #31774062 | C2 | semidirect |
| 5. #31774058 | C2 | semidirect |
| 6. #31774053 | C2 | semidirect |
| 7. #31774050 | C2 | semidirect |
| 8. #31774047 | C2 | semidirect |
| 9. #31773897 | C2 | semidirect |
| 10. #31773859 | C2 | semidirect |
| 11. #451×C271 | C2 | semidirect |
| 17. C2×Q8×D271 | C22 | semidirect |
| 23. C2×#16864644 | C22 | semidirect |
| 24. C2×#16864643 | C22 | semidirect |
| 25. C2×#16864641 | C22 | semidirect |
| 26. C2×#16864637 | C22 | semidirect |
| 27. #22576140 | C22 | semidirect |
| 31. #22576136 | C22 | semidirect |
| 33. C4⋊C4×D271 | C22 | semidirect |
| 35. #22576084 | C22 | semidirect |
| 36. #22576082 | C22 | semidirect |
| 37. #22576080 | C22 | semidirect |
| 39. (C2×D271)⋊C8 | C22 | semidirect |
| 41. C2×Q16×C271 | C22 | semidirect |
| 43. #103×C271 | C22 | semidirect |
| 142. C22×C271 | #137 | semidirect |
| 171. C271 | #3007 | semidirect |
| 179. #451 | D271 | semidirect |
| 197. C2×Q16 | C2×D271 | semidirect |
| 211. #103 | C2×D271 | semidirect |
| 325. C22 | #22576192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864655 | 2 |
| C2×#22576192 | 2 |
| C22⋊Q8×D271 | 2 |
| #31774062 | 2 |
| #31774058 | 2 |
| #31774053 | 2 |
| #31774050 | 2 |
| #31774047 | 2 |
| #31773897 | 2 |
| #31773859 | 2 |
| #451×C271 | 2 |
| #3007 | 271 |