Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
492 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #22608546 | C2 | semidirect |
| 5. #22607831 | C2 | semidirect |
| 6. #22607803 | C2 | semidirect |
| 7. C73×#1485 | C2 | semidirect |
| 197. #1485 | D73 | semidirect |
| 200. C73 | #9312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620087 | 2 |
| #22618360 | 2 |
| #22608546 | 2 |
| #22608366 | 2 |
| #22607831 | 2 |
| #22607803 | 2 |
| C73×#1485 | 2 |
| #9312 | 73 |