Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 53 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×#22576106 | C2 | semidirect |
| 3. C2×#22576103 | C2 | semidirect |
| 4. #31773700 | C2 | semidirect |
| 5. #31773697 | C2 | semidirect |
| 6. C22⋊(C271⋊C16) | C2 | semidirect |
| 7. #467×C271 | C2 | semidirect |
| 85. C271 | #2189 | semidirect |
| 90. #467 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576182 | 2 |
| C2×#22576106 | 2 |
| C2×#22576103 | 2 |
| #31773700 | 2 |
| #31773697 | 2 |
| C22⋊(C271⋊C16) | 2 |
| #467×C271 | 2 |
| #2189 | 271 |