Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
514 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 151 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. #22612204 | C2 | semidirect |
| 4. #22612183 | C2 | semidirect |
| 5. #22612159 | C2 | semidirect |
| 7. #22611787 | C2 | semidirect |
| 9. C73×#2241 | C2 | semidirect |
| 130. C4×D73 | Q32 | semidirect |
| 163. #2241 | D73 | semidirect |
| 167. C73 | #33734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620518 | 2 |
| #22620515 | 2 |
| #22612204 | 2 |
| #22612183 | 2 |
| #22612159 | 2 |
| #22612021 | 2 |
| #22611787 | 2 |
| C4×C16×D73 | 2 |
| C73×#2241 | 2 |
| #33734 | 73 |