Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
398 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 169 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 |
|---|---|---|
| 9. #11763912 | C4 | semidirect |
| 11. C4×#63241 | C4 | semidirect |
| 58. #63241 | C4⋊C4 | semidirect |
| 59. #63225 | C16 | semidirect |
| 101. Dic17 | C4×C16 | semidirect |
| 144. C17 | C16×C4⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763912 | 2 |
| C2×C4×#63241 | 2 |
| #14545854 | 2 |
| #14544576 | 2 |
| C16×C4⋊C4 | 17 |