Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
224 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 224 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 |
|---|---|---|
| 3. #14543818 | C2 | semidirect |
| 4. #14543817 | C2 | semidirect |
| 5. #14543816 | C2 | semidirect |
| 6. #14543815 | C2 | semidirect |
| 64. C16×C17 | M16 | semidirect |
| 66. #63214 | M16 | semidirect |
| 148. C17 | #12025 | semidirect |
| 171. C16 | #63247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544346 | 2 |
| #14544341 | 2 |
| #14543818 | 2 |
| #14543817 | 2 |
| #14543816 | 2 |
| #14543815 | 2 |
| M32×Dic17 | 2 |
| #12025 | 17 |