Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
426 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22619032 | C2 | semidirect |
| 3. #22608525 | C2 | semidirect |
| 6. #22607768 | C2 | semidirect |
| 7. C73×#1278 | C2 | semidirect |
| 186. #1278 | D73 | semidirect |
| 187. C73 | #9070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620254 | 2 |
| #22619032 | 2 |
| #22608525 | 2 |
| #22608349 | 2 |
| #22608347 | 2 |
| #22607768 | 2 |
| C73×#1278 | 2 |
| #9070 | 73 |