Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
836 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 173 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×#22576160 | C2 | semidirect |
| 3. C2×#22576148 | C2 | semidirect |
| 4. C2×#22576139 | C2 | semidirect |
| 5. #31773813 | C2 | semidirect |
| 6. #31773803 | C2 | semidirect |
| 7. #31773799 | C2 | semidirect |
| 8. #31773771 | C2 | semidirect |
| 9. C4×C22⋊C4×C271 | C2 | semidirect |
| 106. C2×C4×C271 | #41 | semidirect |
| 136. C271 | #2432 | semidirect |
| 146. C4×C22⋊C4 | D271 | semidirect |
| 243. C2×C4 | #16864654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864654 | 2 |
| C2×#22576160 | 2 |
| C2×#22576148 | 2 |
| C2×#22576139 | 2 |
| #31773813 | 2 |
| #31773803 | 2 |
| #31773799 | 2 |
| #31773771 | 2 |
| C4×C22⋊C4×C271 | 2 |
| #2432 | 271 |