Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
764 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22617958 | C2 | semidirect |
| 3. #22609849 | C2 | semidirect |
| 4. #22608464 | C2 | semidirect |
| 5. #22608461 | C2 | semidirect |
| 6. #22607840 | C2 | semidirect |
| 7. C73×#3007 | C2 | semidirect |
| 256. #3007 | D73 | semidirect |
| 263. C73 | #9981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619183 | 2 |
| #22617958 | 2 |
| #22609849 | 2 |
| #22608464 | 2 |
| #22608461 | 2 |
| #22607840 | 2 |
| C73×#3007 | 2 |
| #9981 | 73 |