Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
420 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 80 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. #22625814 | C2 | semidirect |
| 3. #22625019 | C2 | semidirect |
| 11. C2×#14556598 | C4 | semidirect |
| 15. #17988610 | C4 | semidirect |
| 17. C2×#14556501 | C4 | semidirect |
| 18. #408×C73 | C4 | semidirect |
| 140. C73 | #12808 | semidirect |
| 150. #408 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626202 | 2 |
| #22625814 | 2 |
| #22625019 | 2 |
| #22618646 | 2 |
| #12808 | 73 |