Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
356 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 145 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. #31774300 | C2 | semidirect |
| 3. #31774297 | C2 | semidirect |
| 4. #31774295 | C2 | semidirect |
| 7. #498×C271 | C2 | semidirect |
| 28. C8×D271 | Q8 | semidirect |
| 67. C271 | #3160 | semidirect |
| 73. #498 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774452 | 2 |
| #31774300 | 2 |
| #31774297 | 2 |
| #31774295 | 2 |
| #31773932 | 2 |
| C4×C8×D271 | 2 |
| #498×C271 | 2 |
| #3160 | 271 |