Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 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. #31773939 | C2 | semidirect |
| 3. C2×#22576086 | C2 | semidirect |
| 4. #31773899 | C2 | semidirect |
| 5. #31773800 | C2 | semidirect |
| 6. #31773658 | C2 | semidirect |
| 7. C2×#100×C271 | C2 | semidirect |
| 61. M16×C271 | D4 | semidirect |
| 130. C271 | #2037 | semidirect |
| 136. C2×#100 | D271 | semidirect |
| 181. M16 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774464 | 2 |
| #31773939 | 2 |
| C2×#22576086 | 2 |
| #31773899 | 2 |
| #31773800 | 2 |
| #31773658 | 2 |
| C2×#100×C271 | 2 |
| #2037 | 271 |