Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C2×#22576084 | C2 | semidirect |
| 4. C2×#22576079 | C2 | semidirect |
| 5. #31773665 | C2 | semidirect |
| 6. #31773661 | C2 | semidirect |
| 24. #137×C271 | C4 | semidirect |
| 116. C271 | #1908 | semidirect |
| 128. #137 | Dic271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576167 | 2 |
| #31773898 | 2 |
| C2×#22576084 | 2 |
| C2×#22576079 | 2 |
| #31773665 | 2 |
| #31773661 | 2 |
| C2×#137×C271 | 2 |
| #1908 | 271 |