Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31774247 | C2 | semidirect |
| 3. #31774230 | C2 | semidirect |
| 4. #31774192 | C2 | semidirect |
| 5. #31774136 | C2 | semidirect |
| 6. #31774104 | C2 | semidirect |
| 7. #31774053 | C2 | semidirect |
| 8. C4×#16864644 | C2 | semidirect |
| 10. C2×#22576084 | C2 | semidirect |
| 92. D4×C271 | Q16 | semidirect |
| 122. C271 | #3299 | semidirect |
| 208. D4 | #16864644 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774604 | 2 |
| #31774247 | 2 |
| #31774230 | 2 |
| #31774192 | 2 |
| #31774136 | 2 |
| #31774104 | 2 |
| #31774053 | 2 |
| C4×#16864644 | 2 |
| D4×C271⋊C8 | 2 |
| C2×#22576084 | 2 |
| D4×Q8×C271 | 2 |
| #3299 | 271 |