Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
368 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 86 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. #14545148 | C2 | semidirect |
| 2. #14544339 | C2 | semidirect |
| 3. #14543744 | C2 | semidirect |
| 4. #14543743 | C2 | semidirect |
| 70. Q16×C17 | M16 | semidirect |
| 91. D136 | M16 | semidirect |
| 203. C17 | #11666 | semidirect |
| 216. Q16 | #63243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545148 | 2 |
| #14544339 | 2 |
| #14543744 | 2 |
| #14543743 | 2 |
| C4×#10587605 | 2 |
| #11666 | 17 |