Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C22×#16864644 | C2 | semidirect |
| 3. #31774276 | C2 | semidirect |
| 4. #31774136 | C2 | semidirect |
| 5. #31774107 | C2 | semidirect |
| 6. #31774104 | C2 | semidirect |
| 7. #31774053 | C2 | semidirect |
| 8. #31774052 | C2 | semidirect |
| 9. C4×#16864644 | C2 | semidirect |
| 52. #16864644 | D4 | direct (N × H) |
| 100. D4×C271 | Q16 | semidirect |
| 113. C22×C271 | C2×Q16 | semidirect |
| 120. C4×C271 | C2×Q16 | semidirect |
| 130. C271 | D4×Q16 | semidirect |
| 224. D4 | #16864644 | direct (N × H) |
| 244. C22 | C2×#16864644 | semidirect |
| 254. C4 | C2×#16864644 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864644 | 2 |
| D4×Dic542 | 2 |
| #31774276 | 2 |
| #31774136 | 2 |
| #31774107 | 2 |
| #31774104 | 2 |
| #31774053 | 2 |
| #31774052 | 2 |
| C4×#16864644 | 2 |
| D4×C271⋊C8 | 2 |
| D4×Q8×C271 | 2 |
| D4×Q16 | 271 |