Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
384 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C2×#22576151 | C2 | semidirect |
| 3. #31774207 | C2 | semidirect |
| 4. #31774203 | C2 | semidirect |
| 5. #31774200 | C2 | semidirect |
| 6. #31774196 | C2 | semidirect |
| 7. #31773940 | C2 | semidirect |
| 8. #31773920 | C2 | semidirect |
| 11. #428×C271 | C2 | semidirect |
| 135. C271 | #3080 | semidirect |
| 144. #428 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576151 | 2 |
| #31774365 | 2 |
| #31774207 | 2 |
| #31774203 | 2 |
| #31774200 | 2 |
| #31774196 | 2 |
| #31773940 | 2 |
| #31773920 | 2 |
| #31773899 | 2 |
| #31773896 | 2 |
| #428×C271 | 2 |
| #3080 | 271 |