Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
712 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 86 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. #22626519 | C2 | semidirect |
| 2. #22625772 | C2 | semidirect |
| 3. #22625327 | C2 | semidirect |
| 4. #22625206 | C2 | semidirect |
| 5. #22624803 | C2 | semidirect |
| 6. #22624773 | C2 | semidirect |
| 23. C22×#11924016 | C4 | semidirect |
| 29. C2×#14556516 | C4 | semidirect |
| 30. C2×#14556512 | C4 | semidirect |
| 32. C22×D8×C73 | C4 | semidirect |
| 289. C73 | #9241 | semidirect |
| 292. C22×D8 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626519 | 2 |
| #22625772 | 2 |
| #22625327 | 2 |
| #22625206 | 2 |
| #22624803 | 2 |
| #22624773 | 2 |
| C2×#17988729 | 2 |
| #9241 | 73 |