Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
472 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22608265 | C2 | semidirect |
| 3. #22607936 | C2 | semidirect |
| 4. #22607933 | C2 | semidirect |
| 5. C73×#1822 | C2 | semidirect |
| 184. #1822 | D73 | semidirect |
| 188. C73 | #11804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22613167 | 2 |
| #22608265 | 2 |
| #22607936 | 2 |
| #22607933 | 2 |
| C73×#1822 | 2 |
| #11804 | 73 |