Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1170 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 147 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. #22609693 | C2 | semidirect |
| 3. C2×#17988326 | C2 | semidirect |
| 4. C73×#1749 | C2 | semidirect |
| 15. C2×#14556502 | C22 | semidirect |
| 20. C2×#97×C73 | C22 | semidirect |
| 179. C22×C73 | #329 | semidirect |
| 214. #1749 | D73 | semidirect |
| 216. C73 | #8334 | semidirect |
| 230. C2×#97 | C2×D73 | semidirect |
| 399. C22 | #17988326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556579 | 2 |
| #22609693 | 2 |
| C2×#17988326 | 2 |
| C73×#1749 | 2 |
| #8334 | 73 |