Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
484 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22608265 | C2 | semidirect |
| 3. #22607957 | C2 | semidirect |
| 4. #22607933 | C2 | semidirect |
| 5. C73×#1742 | C2 | semidirect |
| 190. #1742 | D73 | semidirect |
| 194. C73 | #11761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22615497 | 2 |
| #22608265 | 2 |
| #22607957 | 2 |
| #22607933 | 2 |
| C73×#1742 | 2 |
| #11761 | 73 |