Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. #31774365 | C2 | semidirect |
| 3. #31773913 | C2 | semidirect |
| 4. C2×#22576086 | C2 | semidirect |
| 5. #31773870 | C2 | semidirect |
| 6. #31773658 | C2 | semidirect |
| 7. #344×C271 | C2 | semidirect |
| 11. #22576193 | C4 | semidirect |
| 13. #22576188 | C4 | semidirect |
| 37. C2×Dic542 | C2×C4 | semidirect |
| 39. C2×D1084 | C2×C4 | semidirect |
| 64. M16×C271 | C2×C4 | semidirect |
| 129. C271 | #1906 | semidirect |
| 136. #344 | D271 | semidirect |
| 185. M16 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774697 | 2 |
| #31774365 | 2 |
| #31773913 | 2 |
| C2×#22576086 | 2 |
| #31773870 | 2 |
| #31773658 | 2 |
| #344×C271 | 2 |
| #1906 | 271 |