Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
670 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22608265 | C2 | semidirect |
| 3. #22607862 | C2 | semidirect |
| 4. C73×#1464 | C2 | semidirect |
| 14. #17988313 | C22 | semidirect |
| 18. #324×C73 | C22 | semidirect |
| 175. #1464 | D73 | semidirect |
| 177. C73 | #11509 | semidirect |
| 190. #324 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612511 | 2 |
| #22608265 | 2 |
| #22607862 | 2 |
| C73×#1464 | 2 |
| #11509 | 73 |