Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 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×#22576095 | C2 | semidirect |
| 3. #31773905 | C2 | semidirect |
| 4. C2×#22576078 | C2 | semidirect |
| 6. #31773853 | C2 | semidirect |
| 12. C2×#16864642 | C4 | semidirect |
| 106. C271 | #1977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864642 | 2 |
| C2×#22576095 | 2 |
| #31773905 | 2 |
| C2×#22576078 | 2 |
| C2×#22576077 | 2 |
| #31773853 | 2 |
| #418×C271 | 2 |
| #1977 | 271 |