Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
492 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
| 4. #31774153 | C2 | direct (N × H) |
| 5. C2×#22576091 | C2 | semidirect |
| 6. C2×#22576084 | C2 | semidirect |
| 7. C2×#22576083 | C2 | semidirect |
| 11. C2×#16864644 | C22 | semidirect |
| 21. #22576091 | C22 | semidirect |
| 22. #22576084 | C22 | semidirect |
| 23. #22576083 | C22 | semidirect |
| 111. C2×C271 | #470 | semidirect |
| 115. C271 | C2×#470 | semidirect |
| 227. C2 | #31774153 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864644 | 2 |
| C22×#16864638 | 2 |
| C2×#22576139 | 2 |
| #31774153 | 2 |
| C2×#22576091 | 2 |
| C2×#22576084 | 2 |
| C2×#22576083 | 2 |
| C2×C22⋊Q8×C271 | 2 |
| C2×#470 | 271 |