Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22609722 | C2 | semidirect |
| 3. #22608248 | C2 | semidirect |
| 4. #22607959 | C2 | semidirect |
| 5. #22607957 | C2 | semidirect |
| 6. #22607934 | C2 | semidirect |
| 7. C73×#1345 | C2 | semidirect |
| 216. #1345 | D73 | semidirect |
| 217. C73 | #11737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22615823 | 2 |
| #22609722 | 2 |
| #22608248 | 2 |
| #22607959 | 2 |
| #22607957 | 2 |
| #22607934 | 2 |
| C73×#1345 | 2 |
| #11737 | 73 |