Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
400 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 400 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. C22⋊C16×D73 | C2 | semidirect |
| 3. #22609968 | C2 | semidirect |
| 4. #22607950 | C2 | semidirect |
| 5. #22607948 | C2 | semidirect |
| 6. #22607946 | C2 | semidirect |
| 7. C73×#1349 | C2 | semidirect |
| 185. #1349 | D73 | semidirect |
| 186. C73 | #11893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619510 | 2 |
| C22⋊C16×D73 | 2 |
| #22609968 | 2 |
| #22607950 | 2 |
| #22607948 | 2 |
| #22607946 | 2 |
| C73×#1349 | 2 |
| #11893 | 73 |