Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
380 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 3. #31774304 | C2 | semidirect |
| 4. #31774302 | C2 | semidirect |
| 5. #31774300 | C2 | semidirect |
| 6. #31774293 | C2 | semidirect |
| 9. #498×C271 | C2 | semidirect |
| 43. #16864637 | Q8 | semidirect |
| 79. C271⋊C8 | C2×Q8 | semidirect |
| 87. C8×C271 | C2×Q8 | semidirect |
| 106. C271 | #3165 | semidirect |
| 114. #498 | D271 | semidirect |
| 194. C8 | Q8×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774452 | 2 |
| C4⋊Q8×D271 | 2 |
| #31774304 | 2 |
| #31774302 | 2 |
| #31774300 | 2 |
| #31774293 | 2 |
| #31773936 | 2 |
| C4×#16864637 | 2 |
| #498×C271 | 2 |
| #3165 | 271 |