Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
396 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 1. #22611494 | C2 | semidirect |
| 2. #22611469 | C2 | semidirect |
| 4. #22607757 | C2 | semidirect |
| 5. #22607754 | C2 | semidirect |
| 194. C73 | #7834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611494 | 2 |
| #22611469 | 2 |
| #22611464 | 2 |
| #22607757 | 2 |
| #22607754 | 2 |
| #22607752 | 2 |
| C73×#2808 | 2 |
| #7834 | 73 |