Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
424 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 108. C4⋊C4×C73 | Q16 | semidirect |
| 188. C73 | #7783 | semidirect |
| 288. C4⋊C4 | #11924018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22617884 | 2 |
| #22611256 | 2 |
| #22611031 | 2 |
| #22607756 | 2 |
| #22607754 | 2 |
| #22607753 | 2 |
| C73×#2058 | 2 |
| #7783 | 73 |