Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
218 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. #22608005 | C2 | semidirect |
| 4. #22607986 | C2 | semidirect |
| 5. C73×#2252 | C2 | semidirect |
| 49. C16×C73 | SD16 | semidirect |
| 81. #2252 | D73 | semidirect |
| 86. C73 | #12454 | semidirect |
| 130. C16 | #11924015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611764 | 2 |
| #22609317 | 2 |
| #22608005 | 2 |
| #22607986 | 2 |
| C73×#2252 | 2 |
| #12454 | 73 |