Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
576 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22608555 | C2 | semidirect |
| 3. #22608438 | C2 | semidirect |
| 4. #22607824 | C2 | semidirect |
| 5. C73×#2372 | C2 | semidirect |
| 9. #17988982 | C4 | semidirect |
| 10. #17988977 | C4 | semidirect |
| 33. #14556591 | C2×C4 | semidirect |
| 34. #14556588 | C2×C4 | semidirect |
| 41. #14556502 | C2×C4 | semidirect |
| 172. #2372 | D73 | semidirect |
| 176. C73 | #9441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620395 | 2 |
| #22608555 | 2 |
| #22608438 | 2 |
| #22607824 | 2 |
| C73×#2372 | 2 |
| #9441 | 73 |