Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
480 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 480 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 |
|---|---|---|
| 2. C2×#22576160 | C2 | semidirect |
| 4. #31774108 | C2 | semidirect |
| 5. #31774103 | C2 | semidirect |
| 6. #31773907 | C2 | semidirect |
| 7. #423×C271 | C2 | semidirect |
| 87. C4×C271 | #137 | semidirect |
| 97. C271 | #3039 | semidirect |
| 104. #423 | D271 | semidirect |
| 188. C4 | #22576193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576193 | 2 |
| C2×#22576160 | 2 |
| C4×#16864654 | 2 |
| #31774108 | 2 |
| #31774103 | 2 |
| #31773907 | 2 |
| #423×C271 | 2 |
| #3039 | 271 |