Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
440 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22611602 | C2 | semidirect |
| 3. #22610476 | C2 | semidirect |
| 4. #22610459 | C2 | semidirect |
| 5. #22610219 | C2 | semidirect |
| 6. #22608061 | C2 | semidirect |
| 7. C73×#2122 | C2 | semidirect |
| 204. #2122 | D73 | semidirect |
| 209. C73 | #13432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620792 | 2 |
| #22611602 | 2 |
| #22610476 | 2 |
| #22610459 | 2 |
| #22610219 | 2 |
| #22608061 | 2 |
| C73×#2122 | 2 |
| #13432 | 73 |