Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
374 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 101 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×#22576125 | C2 | semidirect |
| 3. C2×#22576085 | C2 | semidirect |
| 5. #31773659 | C2 | semidirect |
| 6. #31773651 | C2 | semidirect |
| 11. C2×#16864642 | C4 | semidirect |
| 65. Dic542 | C22⋊C4 | semidirect |
| 77. C2×Dic271 | SD16 | semidirect |
| 132. C271 | #1880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864642 | 2 |
| C2×#22576125 | 2 |
| C2×#22576085 | 2 |
| #31773800 | 2 |
| #31773659 | 2 |
| #31773651 | 2 |
| C2×#102×C271 | 2 |
| #1880 | 271 |