Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 4. #31774191 | C2 | semidirect |
| 5. #31774106 | C2 | semidirect |
| 8. #31773991 | C2 | semidirect |
| 9. #31773989 | C2 | semidirect |
| 91. C2×Dic271 | Q16 | semidirect |
| 127. C271 | #3104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774449 | 2 |
| C2×#22576125 | 2 |
| #31774232 | 2 |
| #31774191 | 2 |
| #31774106 | 2 |
| #31774055 | 2 |
| #31774052 | 2 |
| #31773991 | 2 |
| #31773989 | 2 |
| #31773947 | 2 |
| #484×C271 | 2 |
| #3104 | 271 |