Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
406 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 1. #22626290 | C2 | semidirect |
| 2. #22625494 | C2 | semidirect |
| 3. #22624944 | C2 | semidirect |
| 4. #22624943 | C2 | semidirect |
| 7. #17989508 | C22 | semidirect |
| 11. #17989449 | C22 | semidirect |
| 168. C73 | #11957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626290 | 2 |
| #22625494 | 2 |
| #22624944 | 2 |
| #22624943 | 2 |
| #495×D73 | 2 |
| #11957 | 73 |