Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
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. #17989690 | C4 | semidirect |
| 11. C4×#11924040 | C4 | semidirect |
| 41. #11924040 | C4⋊C4 | semidirect |
| 57. #11924007 | C16 | semidirect |
| 95. Dic73 | C4×C16 | semidirect |
| 111. C73 | C16×C4⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989690 | 2 |
| C2×C4×#11924040 | 2 |
| #22627001 | 2 |
| #22625723 | 2 |
| C16×C4⋊C4 | 73 |