Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
294 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 76 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. #14545205 | C2 | semidirect |
| 2. #14545135 | C2 | semidirect |
| 3. #14543938 | C2 | semidirect |
| 6. #11763742 | C22 | semidirect |
| 9. #11763736 | C22 | semidirect |
| 14. #11763242 | C4 | semidirect |
| 17. C2×D272 | C4 | semidirect |
| 19. C2×C17×Q32 | C4 | semidirect |
| 117. C2×Q32 | #595 | semidirect |
| 157. C17 | #13622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545205 | 2 |
| #14545135 | 2 |
| #14543938 | 2 |
| C2×#11763242 | 2 |
| #13622 | 17 |