Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
462 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 155 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×Dic136 | C2 | semidirect |
| 2. #14531101 | C2 | direct (N × H) |
| 3. C2×#11762649 | C2 | semidirect |
| 4. C2×#11762647 | C2 | semidirect |
| 5. C2×#11762643 | C2 | semidirect |
| 11. C2×Dic136 | C22 | semidirect |
| 12. #11762649 | C22 | semidirect |
| 13. #11762647 | C22 | semidirect |
| 14. #11762643 | C22 | semidirect |
| 131. C2×C17 | #2264 | semidirect |
| 158. C17 | C2×#2264 | semidirect |
| 219. C2 | #14531101 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic136 | 2 |
| #14531101 | 2 |
| C2×#11762649 | 2 |
| C2×#11762647 | 2 |
| C2×#11762643 | 2 |
| C2×C17×#508 | 2 |
| C2×#2264 | 17 |