Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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×#17988407 | C2 | semidirect |
| 3. C2×#17988399 | C2 | semidirect |
| 4. #22611648 | C2 | semidirect |
| 5. #22611647 | C2 | semidirect |
| 6. #22609813 | C2 | semidirect |
| 7. C2×#361×C73 | C2 | semidirect |
| 13. #17988962 | C4 | semidirect |
| 46. #14556525 | D4 | semidirect |
| 65. #108×C73 | D4 | semidirect |
| 176. C2×#361 | D73 | semidirect |
| 180. C73 | #13261 | semidirect |
| 232. #108 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988962 | 2 |
| C2×#17988407 | 2 |
| C2×#17988399 | 2 |
| #22611648 | 2 |
| #22611647 | 2 |
| #22609813 | 2 |
| C2×#361×C73 | 2 |
| #13261 | 73 |