Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
674 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 211 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. #22610496 | C2 | semidirect |
| 3. #22610494 | C2 | semidirect |
| 130. C73 | #21917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612415 | 2 |
| #22610496 | 2 |
| #22610494 | 2 |
| #22610002 | 2 |
| #22609913 | 2 |
| #22609695 | 2 |
| C73×#1818 | 2 |
| #21917 | 73 |