Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
302 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22622504 | C2 | semidirect |
| 2. #22612174 | C2 | semidirect |
| 3. #22611972 | C2 | semidirect |
| 5. #22607900 | C2 | semidirect |
| 6. #22607888 | C2 | semidirect |
| 7. C73×#1363 | C2 | semidirect |
| 151. #1363 | D73 | semidirect |
| 154. C73 | #12349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622504 | 2 |
| #22612174 | 2 |
| #22611972 | 2 |
| #22609411 | 2 |
| #22607900 | 2 |
| #22607888 | 2 |
| C73×#1363 | 2 |
| #12349 | 73 |