Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1516 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1516 conjugacy classes of subgroups — too many to draw. Only its 171 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. #22609928 | C2 | semidirect |
| 3. C2×#17988331 | C2 | semidirect |
| 4. C2×#17988316 | C2 | semidirect |
| 5. C73×#1957 | C2 | semidirect |
| 9. #17989222 | C4 | semidirect |
| 13. C2×C4⋊#10596831 | C22 | semidirect |
| 20. C2×C4×C8×C73 | C22 | semidirect |
| 21. #384×C73 | C22 | semidirect |
| 158. D292 | #102 | semidirect |
| 200. #1957 | D73 | semidirect |
| 204. C73 | #8443 | semidirect |
| 216. C2×C4×C8 | C2×D73 | semidirect |
| 217. #384 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989222 | 2 |
| #22609928 | 2 |
| C2×#17988331 | 2 |
| C2×#17988316 | 2 |
| C73×#1957 | 2 |
| #8443 | 73 |