Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22611696 | C2 | semidirect |
| 5. #22610056 | C2 | semidirect |
| 6. #22608038 | C2 | semidirect |
| 7. C73×#1383 | C2 | semidirect |
| 11. #17988698 | C4 | semidirect |
| 12. #17988693 | C4 | semidirect |
| 157. #1383 | 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 |
|---|---|
| #22618814 | 2 |
| #22611696 | 2 |
| #22611668 | 2 |
| #22611658 | 2 |
| #22610056 | 2 |
| #22608038 | 2 |
| C73×#1383 | 2 |
| #12828 | 73 |