Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
248 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 71 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. Q8×#63214 | C2 | semidirect |
| 3. #14528144 | C2 | semidirect |
| 4. #14526855 | C2 | semidirect |
| 5. #14526830 | C2 | semidirect |
| 6. #14526829 | C2 | semidirect |
| 7. C17×#1668 | C2 | semidirect |
| 71. #63214 | SD16 | semidirect |
| 76. Q8×C17 | D16 | semidirect |
| 101. #1668 | D17 | semidirect |
| 161. C17 | #12439 | semidirect |
| 192. Q8 | #10587497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531033 | 2 |
| Q8×#63214 | 2 |
| #14528144 | 2 |
| #14526855 | 2 |
| #14526830 | 2 |
| #14526829 | 2 |
| C17×#1668 | 2 |
| #12439 | 17 |