Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. #31774305 | C2 | semidirect |
| 4. #31774304 | C2 | semidirect |
| 5. #31774298 | C2 | semidirect |
| 6. #31774297 | C2 | semidirect |
| 48. #16864638 | Q8 | semidirect |
| 72. M16×C271 | Q8 | semidirect |
| 124. C271 | #3166 | semidirect |
| 176. M16 | Dic542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774450 | 2 |
| C2×#22576151 | 2 |
| #31774305 | 2 |
| #31774304 | 2 |
| #31774298 | 2 |
| #31774297 | 2 |
| #31773940 | 2 |
| #31773939 | 2 |
| #31773937 | 2 |
| M16×Dic271 | 2 |
| #428×C271 | 2 |
| #3166 | 271 |