Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
314 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 314 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 |
|---|---|---|
| 1. #22622323 | C2 | semidirect |
| 2. #22612156 | C2 | semidirect |
| 3. #22611972 | C2 | semidirect |
| 5. #22607894 | C2 | semidirect |
| 6. #22607885 | C2 | semidirect |
| 7. C73×#1365 | C2 | semidirect |
| 102. D292 | SD32 | semidirect |
| 139. #1365 | D73 | semidirect |
| 142. C73 | #12342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622323 | 2 |
| #22612156 | 2 |
| #22611972 | 2 |
| #22609287 | 2 |
| #22607894 | 2 |
| #22607885 | 2 |
| C73×#1365 | 2 |
| #12342 | 73 |