Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
582 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 102 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. C2×#17989597 | C2 | semidirect |
| 2. C2×#17989499 | C2 | semidirect |
| 3. #22626156 | C2 | semidirect |
| 4. #22624988 | C2 | semidirect |
| 17. #17988824 | C4 | semidirect |
| 18. #17988823 | C4 | semidirect |
| 21. #17988820 | C4 | semidirect |
| 24. #466×C73 | C4 | semidirect |
| 34. #14556660 | D4 | semidirect |
| 216. C73 | #12992 | semidirect |
| 227. #466 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989597 | 2 |
| C2×#17989499 | 2 |
| #22626156 | 2 |
| #22624988 | 2 |
| #466×D73 | 2 |
| #12992 | 73 |