Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
558 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 97 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. #14545929 | C2 | semidirect |
| 4. #14545795 | C2 | semidirect |
| 54. C17×#99 | C8 | semidirect |
| 55. #10587505 | C8 | semidirect |
| 56. #10587477 | C8 | semidirect |
| 103. C22⋊C4×C17 | C2×C8 | semidirect |
| 104. C22⋊Dic17 | C2×C8 | semidirect |
| 107. C23×C17 | C4⋊C8 | semidirect |
| 115. C22×D17 | C4⋊C8 | semidirect |
| 145. C2×C4×C17 | C4⋊C8 | semidirect |
| 149. C2×Dic17 | C4⋊C8 | semidirect |
| 242. #99 | #3633 | semidirect |
| 250. C17 | #8851 | semidirect |
| 295. C22⋊C4 | C2×#3633 | semidirect |
| 311. C23 | C4⋊#3633 | semidirect |
| 343. C2×C4 | C4⋊#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14546026 | 2 |
| #14545930 | 2 |
| #14545929 | 2 |
| #14545795 | 2 |
| #99×#595 | 2 |
| #8851 | 17 |