Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
542 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22611177 | C2 | semidirect |
| 3. #22611068 | C2 | semidirect |
| 4. #22611068 | C2 | semidirect |
| 5. #22607751 | C2 | semidirect |
| 6. #22607751 | C2 | semidirect |
| 7. C73×#1271 | C2 | semidirect |
| 231. #1271 | D73 | semidirect |
| 234. C73 | #7762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22616293 | 2 |
| #22611177 | 2 |
| #22611068 | 2 |
| #22607751 | 2 |
| C73×#1271 | 2 |
| #7762 | 73 |