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 |
|---|---|---|
| 1. #14541790 | C2 | semidirect |
| 3. #14531012 | C2 | semidirect |
| 4. #14530927 | C2 | semidirect |
| 7. Q8×C16×C17 | C2 | semidirect |
| 73. Q8×C17 | SD32 | semidirect |
| 94. Q8×C16 | D17 | semidirect |
| 149. C17 | #33926 | semidirect |
| 179. Q8 | #10587471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541790 | 2 |
| Q8×D136 | 2 |
| #14531012 | 2 |
| #14530927 | 2 |
| #14530830 | 2 |
| C4×#10587471 | 2 |
| Q8×C16×C17 | 2 |
| #33926 | 17 |