Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
548 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 238 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. Q8×#63216 | C2 | semidirect |
| 2. #14545170 | C2 | semidirect |
| 3. #14545148 | C2 | semidirect |
| 4. C4×#10587530 | C2 | semidirect |
| 58. #63216 | #41 | semidirect |
| 61. Q8×C17 | M32 | semidirect |
| 129. C17 | #33485 | semidirect |
| 152. Q8 | #10587530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#63216 | 2 |
| #14545170 | 2 |
| #14545148 | 2 |
| C4×#10587530 | 2 |
| C8×#63256 | 2 |
| #33485 | 17 |