Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
368 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 368 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. #31774276 | C2 | semidirect |
| 4. #31774249 | C2 | semidirect |
| 5. #31774247 | C2 | semidirect |
| 7. C4×#16864644 | C2 | semidirect |
| 79. C2×C4×C271 | Q16 | semidirect |
| 104. C271 | #3170 | semidirect |
| 182. C2×C4 | #16864644 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774454 | 2 |
| #31774300 | 2 |
| #31774276 | 2 |
| #31774249 | 2 |
| #31774247 | 2 |
| #31774136 | 2 |
| C4×#16864644 | 2 |
| C2×C4×C271⋊C8 | 2 |
| #533×C271 | 2 |
| #3170 | 271 |