Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22611638 | C2 | semidirect |
| 4. C2×#17988372 | C2 | semidirect |
| 5. #22609974 | C2 | semidirect |
| 6. #22608026 | C2 | semidirect |
| 7. C73×#2145 | C2 | semidirect |
| 178. #2145 | D73 | semidirect |
| 183. C73 | #13401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619647 | 2 |
| #22611704 | 2 |
| #22611638 | 2 |
| C2×#17988372 | 2 |
| #22609974 | 2 |
| #22608026 | 2 |
| C73×#2145 | 2 |
| #13401 | 73 |