Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
428 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22610776 | C2 | semidirect |
| 4. #22608681 | C2 | semidirect |
| 6. #22607834 | C2 | semidirect |
| 7. C73×#1988 | C2 | semidirect |
| 191. #1988 | D73 | semidirect |
| 197. C73 | #10503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621052 | 2 |
| #22610849 | 2 |
| #22610776 | 2 |
| #22608681 | 2 |
| #22608606 | 2 |
| #22607834 | 2 |
| C73×#1988 | 2 |
| #10503 | 73 |