Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
912 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 119 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. #22609919 | C2 | semidirect |
| 3. #22609863 | C2 | semidirect |
| 4. #22607799 | C2 | semidirect |
| 5. C73×#2973 | C2 | semidirect |
| 11. #17988504 | C4 | semidirect |
| 12. #17988496 | C4 | semidirect |
| 47. C22×C8×C73 | D4 | semidirect |
| 213. #2973 | D73 | semidirect |
| 218. C73 | #9472 | semidirect |
| 247. C22×C8 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22613287 | 2 |
| #22609919 | 2 |
| #22609863 | 2 |
| #22607799 | 2 |
| C73×#2973 | 2 |
| #9472 | 73 |