Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
434 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 434 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 |
| 8. #17988526 | C4 | semidirect |
| 10. #17988517 | C4 | semidirect |
| 17. C4×C22⋊Dic73 | C4 | semidirect |
| 188. C73 | #11822 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22613190 | 2 |
| #22609919 | 2 |
| #22607956 | 2 |
| #22607932 | 2 |
| C73×#1466 | 2 |
| #11822 | 73 |