Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
286 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22612214 | C2 | semidirect |
| 3. #22609446 | C2 | semidirect |
| 4. #22607982 | C2 | semidirect |
| 5. #22607912 | C2 | semidirect |
| 84. D8×C73 | Q16 | semidirect |
| 143. C73 | #12414 | semidirect |
| 205. D8 | #11924018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622887 | 2 |
| #22612214 | 2 |
| #22609446 | 2 |
| #22607982 | 2 |
| #22607912 | 2 |
| #22607898 | 2 |
| C73×#2226 | 2 |
| #12414 | 73 |