Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #31774452 | C2 | semidirect |
| 3. #31774236 | C2 | semidirect |
| 4. #31774192 | C2 | semidirect |
| 5. #31774188 | C2 | semidirect |
| 6. #31774099 | C2 | semidirect |
| 8. #31774004 | C2 | semidirect |
| 9. #31774000 | C2 | semidirect |
| 10. #31773953 | C2 | semidirect |
| 11. #462×C271 | C2 | semidirect |
| 136. C271 | #3116 | semidirect |
| 143. #462 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774452 | 2 |
| C4×#16864655 | 2 |
| #31774236 | 2 |
| #31774192 | 2 |
| #31774188 | 2 |
| #31774099 | 2 |
| #31774058 | 2 |
| #31774004 | 2 |
| #31774000 | 2 |
| #31773953 | 2 |
| #462×C271 | 2 |
| #3116 | 271 |