Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
412 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 3. C2×#11763700 | C2 | semidirect |
| 4. #14544605 | C2 | semidirect |
| 5. #14543861 | C2 | semidirect |
| 6. #14543854 | C2 | semidirect |
| 18. #11763728 | C4 | semidirect |
| 19. #11763727 | C4 | semidirect |
| 25. #11762617 | C4 | semidirect |
| 26. #11762616 | C4 | semidirect |
| 27. #11762615 | C4 | semidirect |
| 28. C17×#359 | C4 | semidirect |
| 194. #359 | #595 | semidirect |
| 244. C17 | #12651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17⋊#444 | 2 |
| #14545111 | 2 |
| C2×#11763700 | 2 |
| #14544605 | 2 |
| #14543861 | 2 |
| #14543854 | 2 |
| #14530510 | 2 |
| #12651 | 17 |