Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31774626 | C2 | semidirect |
| 3. #31774250 | C2 | semidirect |
| 5. #31774199 | C2 | semidirect |
| 6. #31774183 | C2 | semidirect |
| 7. #31774117 | C2 | semidirect |
| 8. #31774021 | C2 | semidirect |
| 9. C4×#16864644 | C2 | semidirect |
| 10. SD16×Dic271 | C2 | semidirect |
| 117. C271 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774633 | 2 |
| #31774626 | 2 |
| #31774250 | 2 |
| #31774243 | 2 |
| #31774199 | 2 |
| #31774183 | 2 |
| #31774117 | 2 |
| #31774021 | 2 |
| C4×#16864644 | 2 |
| SD16×Dic271 | 2 |
| #460×C271 | 2 |
| #3365 | 271 |