Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
506 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 3. #22607956 | C2 | semidirect |
| 4. #22607932 | C2 | semidirect |
| 6. C2×#14556550 | C4 | semidirect |
| 7. #17988523 | C4 | semidirect |
| 9. #17988512 | C4 | semidirect |
| 14. #17988450 | C4 | semidirect |
| 204. C73 | #11841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22614205 | 2 |
| #22610005 | 2 |
| #22607956 | 2 |
| #22607932 | 2 |
| C2×#323×C73 | 2 |
| #11841 | 73 |