Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
318 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 53 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. #22612146 | C2 | semidirect |
| 3. #22612143 | C2 | semidirect |
| 4. #22611507 | C2 | semidirect |
| 5. #22607915 | C2 | semidirect |
| 6. #22607881 | C2 | semidirect |
| 7. C73×#1339 | C2 | semidirect |
| 152. #1339 | D73 | semidirect |
| 154. C73 | #12307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621308 | 2 |
| #22612146 | 2 |
| #22612143 | 2 |
| #22611507 | 2 |
| #22607915 | 2 |
| #22607881 | 2 |
| C73×#1339 | 2 |
| #12307 | 73 |