Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
506 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 165 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. #14531011 | C2 | semidirect |
| 3. #14530926 | C2 | semidirect |
| 5. Q8×#63214 | C2 | semidirect |
| 7. C17×#3395 | C2 | semidirect |
| 75. Q8×C17 | SD32 | semidirect |
| 89. #3395 | D17 | semidirect |
| 149. C17 | #33926 | semidirect |
| 179. Q8 | #10587499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D136 | 2 |
| #14531011 | 2 |
| #14530926 | 2 |
| #14530826 | 2 |
| Q8×#63214 | 2 |
| C4×#10587499 | 2 |
| C17×#3395 | 2 |
| #33926 | 17 |