Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
510 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. C22×D2168 | C2 | semidirect |
| 2. C2×#22576157 | C2 | semidirect |
| 3. C2×#22576082 | C2 | semidirect |
| 4. #31773799 | C2 | semidirect |
| 5. #336×C271 | C2 | semidirect |
| 32. C2×D1084 | D4 | semidirect |
| 41. C2×C8×C271 | D4 | semidirect |
| 65. C2×C4×C271 | D8 | semidirect |
| 97. C271 | #2011 | semidirect |
| 103. #336 | D271 | semidirect |
| 137. C2×C8 | D1084 | semidirect |
| 163. C2×C4 | D2168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D2168 | 2 |
| C2×#22576157 | 2 |
| C2×#22576082 | 2 |
| #31773799 | 2 |
| #336×C271 | 2 |
| #2011 | 271 |