Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
466 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#17988401 | C2 | semidirect |
| 3. #22611668 | C2 | semidirect |
| 4. #22611660 | C2 | semidirect |
| 5. #22611648 | C2 | semidirect |
| 6. #22610055 | C2 | semidirect |
| 7. C73×#2110 | C2 | semidirect |
| 13. #17988971 | C4 | semidirect |
| 14. #17988964 | C4 | semidirect |
| 62. M32×C73 | D4 | semidirect |
| 64. C2×C16×C73 | D4 | semidirect |
| 180. #2110 | D73 | semidirect |
| 182. C73 | #13215 | semidirect |
| 233. M32 | D292 | semidirect |
| 235. C2×C16 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620417 | 2 |
| C2×#17988401 | 2 |
| #22611668 | 2 |
| #22611660 | 2 |
| #22611648 | 2 |
| #22610055 | 2 |
| C73×#2110 | 2 |
| #13215 | 73 |