Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
438 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22618920 | C2 | semidirect |
| 3. #22608549 | C2 | semidirect |
| 4. C2×#17988326 | C2 | semidirect |
| 5. #22608282 | C2 | semidirect |
| 6. #22607831 | C2 | semidirect |
| 7. C73×#1281 | C2 | semidirect |
| 219. #1281 | D73 | semidirect |
| 220. C73 | #9265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620898 | 2 |
| #22618920 | 2 |
| #22608549 | 2 |
| C2×#17988326 | 2 |
| #22608282 | 2 |
| #22607831 | 2 |
| C73×#1281 | 2 |
| #9265 | 73 |