Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
708 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 2. C4⋊C8×#595 | C2 | semidirect |
| 4. #14543663 | C2 | semidirect |
| 15. #11763667 | C4 | semidirect |
| 18. #11762553 | C4 | semidirect |
| 19. #11762552 | C4 | semidirect |
| 20. C17×#331 | C4 | semidirect |
| 42. #10587544 | C2×C4 | semidirect |
| 45. C17×C4⋊C8 | C2×C4 | semidirect |
| 47. C4⋊#3622 | C2×C4 | semidirect |
| 150. #595 | #331 | direct (N × H) |
| 171. #331 | #595 | direct (N × H) |
| 204. C4⋊C8 | C2×#595 | semidirect |
| 206. C17 | C4×#331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #127×#595 | 2 |
| C4⋊C8×#595 | 2 |
| D17⋊#331 | 2 |
| #14543663 | 2 |
| D17×#331 | 2 |
| C4×#331 | 17 |