Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22611697 | C2 | semidirect |
| 5. #22608036 | C2 | semidirect |
| 6. #22608031 | C2 | semidirect |
| 7. C73×#1833 | C2 | semidirect |
| 12. #17988700 | C4 | semidirect |
| 13. #17988695 | C4 | semidirect |
| 155. #1833 | D73 | semidirect |
| 158. C73 | #12828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618816 | 2 |
| #22611697 | 2 |
| #22611666 | 2 |
| #22611658 | 2 |
| #22608036 | 2 |
| #22608031 | 2 |
| C73×#1833 | 2 |
| #12828 | 73 |