Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
336 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31774299 | C2 | semidirect |
| 3. #31774239 | C2 | semidirect |
| 4. #31774233 | C2 | semidirect |
| 5. #31774205 | C2 | semidirect |
| 6. #31774155 | C2 | semidirect |
| 7. C4×Dic1084 | C2 | semidirect |
| 8. #31773939 | C2 | semidirect |
| 96. C271 | #3352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774587 | 2 |
| #31774299 | 2 |
| #31774239 | 2 |
| #31774233 | 2 |
| #31774205 | 2 |
| #31774155 | 2 |
| C4×Dic1084 | 2 |
| #31773939 | 2 |
| #436×C271 | 2 |
| #3352 | 271 |