Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
218 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 31. Q16×C17 | C16 | semidirect |
| 45. #63216 | Q16 | direct (N × H) |
| 101. C17 | C16×Q16 | semidirect |
| 103. Q16 | #63216 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#63216 | 2 |
| #14543813 | 2 |
| Q8⋊#63216 | 2 |
| C8×#63216 | 2 |
| Q16×#3622 | 2 |
| C16×Q16 | 17 |