Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 2. #31774299 | C2 | semidirect |
| 3. #31774237 | C2 | semidirect |
| 4. #31774231 | C2 | semidirect |
| 5. #31774204 | C2 | semidirect |
| 6. #31774152 | C2 | semidirect |
| 8. #31773938 | C2 | semidirect |
| 9. C4×Q16×C271 | C2 | semidirect |
| 96. C271 | #3352 | semidirect |
| 104. C4×Q16 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774588 | 2 |
| #31774299 | 2 |
| #31774237 | 2 |
| #31774231 | 2 |
| #31774204 | 2 |
| #31774152 | 2 |
| #31773976 | 2 |
| #31773938 | 2 |
| C4×Q16×C271 | 2 |
| #3352 | 271 |