Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31774301 | C2 | semidirect |
| 3. #31774275 | C2 | semidirect |
| 4. #31774246 | C2 | semidirect |
| 7. Q16×Dic271 | C2 | semidirect |
| 8. #31773991 | C2 | semidirect |
| 9. #31773989 | C2 | semidirect |
| 77. C2×Dic271 | Q16 | semidirect |
| 114. C271 | #3170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774449 | 2 |
| #31774301 | 2 |
| #31774275 | 2 |
| #31774246 | 2 |
| #31774138 | 2 |
| #31774136 | 2 |
| Q16×Dic271 | 2 |
| #31773991 | 2 |
| #31773989 | 2 |
| C2×C8×Dic271 | 2 |
| #467×C271 | 2 |
| #3170 | 271 |