Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22610870 | C2 | semidirect |
| 5. #22608359 | C2 | semidirect |
| 6. #22607775 | C2 | semidirect |
| 7. C73×#1301 | C2 | semidirect |
| 94. C2×#10596831 | SD16 | semidirect |
| 191. #1301 | D73 | semidirect |
| 193. C73 | #9047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619963 | 2 |
| #22618648 | 2 |
| #22610870 | 2 |
| #22608581 | 2 |
| #22608359 | 2 |
| #22607775 | 2 |
| C73×#1301 | 2 |
| #9047 | 73 |