Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
336 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22612099 | C2 | semidirect |
| 3. #22609565 | C2 | semidirect |
| 4. #22607969 | C2 | semidirect |
| 5. #22607907 | C2 | semidirect |
| 6. #22607906 | C2 | semidirect |
| 7. C73×#2230 | C2 | semidirect |
| 164. #2230 | D73 | semidirect |
| 169. C73 | #12367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621736 | 2 |
| #22612099 | 2 |
| #22609565 | 2 |
| #22607969 | 2 |
| #22607907 | 2 |
| #22607906 | 2 |
| C73×#2230 | 2 |
| #12367 | 73 |