Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
312 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 312 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. #22611733 | C2 | semidirect |
| 3. #334×D73 | C2 | semidirect |
| 4. #22607984 | C2 | semidirect |
| 5. #22607982 | C2 | semidirect |
| 6. #22607974 | C2 | semidirect |
| 7. C73×#1360 | C2 | semidirect |
| 156. #1360 | D73 | semidirect |
| 157. C73 | #11945 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620498 | 2 |
| #22611733 | 2 |
| #334×D73 | 2 |
| #22607984 | 2 |
| #22607982 | 2 |
| #22607974 | 2 |
| C73×#1360 | 2 |
| #11945 | 73 |