Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
226 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. #14543810 | C2 | semidirect |
| 4. #14543809 | C2 | semidirect |
| 56. C16×C17 | M16 | semidirect |
| 58. #63214 | M16 | semidirect |
| 130. C17 | #12019 | semidirect |
| 151. C16 | #63247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544344 | 2 |
| #14544338 | 2 |
| #14543810 | 2 |
| #14543809 | 2 |
| C2×#11762584 | 2 |
| #12019 | 17 |