Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22611704 | C2 | semidirect |
| 3. #22611660 | C2 | semidirect |
| 4. #22611639 | C2 | semidirect |
| 5. #22609985 | C2 | semidirect |
| 6. #22608025 | C2 | semidirect |
| 7. C73×#2113 | C2 | semidirect |
| 179. #2113 | D73 | semidirect |
| 182. C73 | #13406 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619651 | 2 |
| #22611704 | 2 |
| #22611660 | 2 |
| #22611639 | 2 |
| #22609985 | 2 |
| #22608025 | 2 |
| C73×#2113 | 2 |
| #13406 | 73 |