Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
306 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×#22576087 | C2 | semidirect |
| 2. #31773898 | C2 | semidirect |
| 3. #31773766 | C2 | semidirect |
| 4. #31773666 | C2 | semidirect |
| 26. C4×Dic271 | D4 | semidirect |
| 85. C271 | #2039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576087 | 2 |
| #31773898 | 2 |
| #31773766 | 2 |
| #31773666 | 2 |
| #537×C271 | 2 |
| #2039 | 271 |