Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
820 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 171 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. #22621158 | C2 | semidirect |
| 2. #22620313 | C2 | semidirect |
| 3. #22609265 | C2 | semidirect |
| 4. #22609259 | C2 | semidirect |
| 5. #22609254 | C2 | semidirect |
| 6. #22608569 | C2 | semidirect |
| 7. #22608538 | C2 | semidirect |
| 210. C73 | #19005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621158 | 2 |
| #22620313 | 2 |
| #22609265 | 2 |
| #22609259 | 2 |
| #22609254 | 2 |
| #22608569 | 2 |
| #22608538 | 2 |
| C73×#3531 | 2 |
| #19005 | 73 |