Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
212 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 2. #22608840 | C2 | semidirect |
| 3. #22607997 | C2 | semidirect |
| 4. #22607901 | C2 | semidirect |
| 6. #22607851 | C2 | semidirect |
| 66. C16×C73 | M16 | semidirect |
| 110. C73 | #12087 | semidirect |
| 169. C16 | #11924012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22608845 | 2 |
| #22608840 | 2 |
| #22607997 | 2 |
| #22607901 | 2 |
| #22607898 | 2 |
| #22607851 | 2 |
| C73×#2175 | 2 |
| #12087 | 73 |