Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
224 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #14526857 | C2 | semidirect |
| 5. #14526856 | C2 | semidirect |
| 6. #14526855 | C2 | semidirect |
| 7. C17×#1372 | C2 | semidirect |
| 64. C16×C17 | M16 | semidirect |
| 66. #63214 | M16 | semidirect |
| 93. #1372 | D17 | semidirect |
| 148. C17 | #12025 | semidirect |
| 171. C16 | #63218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587469 | 2 |
| #14527546 | 2 |
| #14527541 | 2 |
| #14526857 | 2 |
| #14526856 | 2 |
| #14526855 | 2 |
| C17×#1372 | 2 |
| #12025 | 17 |