Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
702 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 1. C22×#14556510 | C2 | semidirect |
| 3. C2×#17988383 | C2 | semidirect |
| 4. #22608057 | C2 | semidirect |
| 5. C73×#1784 | C2 | semidirect |
| 48. #14556510 | D4 | semidirect |
| 205. C22×C73 | #355 | semidirect |
| 236. #1784 | D73 | semidirect |
| 238. C73 | #13092 | semidirect |
| 443. C22 | #17988383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556510 | 2 |
| #22613585 | 2 |
| C2×#17988383 | 2 |
| #22608057 | 2 |
| C73×#1784 | 2 |
| #13092 | 73 |