Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
2022 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 2022 conjugacy classes of subgroups — too many to draw. Only its 587 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. #14536975 | C2 | direct (N × H) |
| 2. C2×#11762751 | C2 | semidirect |
| 4. C2×#11762728 | C2 | semidirect |
| 11. #11762751 | C22 | semidirect |
| 13. #11762728 | C22 | semidirect |
| 129. C2×C17 | #2835 | semidirect |
| 154. C17 | C2×#2835 | semidirect |
| 219. C2 | #14536975 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14536975 | 2 |
| C2×#11762751 | 2 |
| C2×#11762734 | 2 |
| C2×#11762728 | 2 |
| C2×#11762681 | 2 |
| C2×C17×#393 | 2 |
| C2×#2835 | 17 |