Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22612533 | C2 | semidirect |
| 4. C2×#17988312 | C2 | semidirect |
| 5. #22607799 | C2 | semidirect |
| 6. #22607798 | C2 | semidirect |
| 11. #17988518 | C4 | semidirect |
| 13. #17988501 | C4 | semidirect |
| 231. C73 | #9206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22615675 | 2 |
| #22612533 | 2 |
| #22608499 | 2 |
| C2×#17988312 | 2 |
| #22607799 | 2 |
| #22607798 | 2 |
| C73×#1519 | 2 |
| #9206 | 73 |