Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #31774597 | C2 | semidirect |
| 2. #31774299 | C2 | semidirect |
| 3. #31774219 | C2 | semidirect |
| 4. #31774209 | C2 | semidirect |
| 5. #31774197 | C2 | semidirect |
| 6. #31774147 | C2 | semidirect |
| 7. #31773976 | C2 | semidirect |
| 8. #31773938 | C2 | semidirect |
| 9. C4×D8×C271 | C2 | semidirect |
| 102. C271 | #3355 | semidirect |
| 110. C4×D8 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774597 | 2 |
| #31774299 | 2 |
| #31774219 | 2 |
| #31774209 | 2 |
| #31774197 | 2 |
| #31774147 | 2 |
| #31773976 | 2 |
| #31773938 | 2 |
| C4×D8×C271 | 2 |
| #3355 | 271 |