Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 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 |
|---|---|---|
| 2. C2×#22576193 | C2 | semidirect |
| 3. C2×#22576139 | C2 | semidirect |
| 4. #31774061 | C2 | semidirect |
| 5. #31774055 | C2 | semidirect |
| 6. #31774050 | C2 | semidirect |
| 7. #31773899 | C2 | semidirect |
| 8. #407×C271 | C2 | semidirect |
| 15. C22×Dic542 | C22 | semidirect |
| 20. C2×Dic1084 | C22 | semidirect |
| 21. C2×#16864643 | C22 | semidirect |
| 25. #22576139 | C22 | semidirect |
| 26. C2×C4⋊Dic271 | C22 | semidirect |
| 29. #22576085 | C22 | semidirect |
| 30. #22576082 | C22 | semidirect |
| 32. C2×M16×C271 | C22 | semidirect |
| 34. C22⋊C8×C271 | C22 | semidirect |
| 126. C22×C271 | #137 | semidirect |
| 146. C271 | #3007 | semidirect |
| 155. #407 | D271 | semidirect |
| 170. C2×M16 | C2×D271 | semidirect |
| 181. C22⋊C8 | C2×D271 | semidirect |
| 277. C22 | #22576193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864654 | 2 |
| C2×#22576193 | 2 |
| C2×#22576139 | 2 |
| #31774061 | 2 |
| #31774055 | 2 |
| #31774050 | 2 |
| #31773899 | 2 |
| #407×C271 | 2 |
| #3007 | 271 |