Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
286 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22612204 | C2 | semidirect |
| 3. #22612084 | C2 | semidirect |
| 5. #22607894 | C2 | semidirect |
| 7. C73×#1365 | C2 | semidirect |
| 127. #1365 | D73 | semidirect |
| 130. C73 | #12398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622323 | 2 |
| #22612204 | 2 |
| #22612084 | 2 |
| #22609331 | 2 |
| #22607894 | 2 |
| #22607885 | 2 |
| C73×#1365 | 2 |
| #12398 | 73 |