Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
540 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 103 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×#17988383 | C2 | semidirect |
| 3. C4×#14556510 | C2 | semidirect |
| 4. C73×#1801 | C2 | semidirect |
| 36. #14556510 | D4 | semidirect |
| 155. C4×C73 | #355 | semidirect |
| 166. #1801 | D73 | semidirect |
| 168. C73 | #13226 | semidirect |
| 320. C4 | #17988383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22614930 | 2 |
| C2×#17988383 | 2 |
| C4×#14556510 | 2 |
| C73×#1801 | 2 |
| #13226 | 73 |