Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
686 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 203 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. C2×#11763211 | C2 | semidirect |
| 3. #14531026 | C2 | direct (N × H) |
| 4. C2×#11762611 | C2 | semidirect |
| 5. C2×C17×#346 | C2 | semidirect |
| 11. #11763211 | C22 | semidirect |
| 16. #11762611 | C22 | semidirect |
| 19. C17×#346 | C22 | semidirect |
| 91. C2×#346 | D17 | semidirect |
| 116. #346 | C2×D17 | semidirect |
| 117. C2×C17 | #2244 | semidirect |
| 144. C17 | C2×#2244 | semidirect |
| 200. C2 | #14531026 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763211 | 2 |
| C2×#11763186 | 2 |
| #14531026 | 2 |
| C2×#11762611 | 2 |
| C2×C17×#346 | 2 |
| C2×#2244 | 17 |