Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
242 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 80 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. #14545170 | C2 | semidirect |
| 2. #14543813 | C2 | semidirect |
| 3. #14543735 | C2 | semidirect |
| 4. C8×#63216 | C2 | semidirect |
| 48. #63216 | D8 | semidirect |
| 61. C8×C17 | M32 | semidirect |
| 110. C17 | #12039 | semidirect |
| 144. C8 | #10587530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545170 | 2 |
| #14543813 | 2 |
| #14543735 | 2 |
| C8×#63216 | 2 |
| #14527578 | 2 |
| #12039 | 17 |