Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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×#17989005 | C2 | semidirect |
| 3. #22611668 | C2 | semidirect |
| 4. C2×#17988393 | C2 | semidirect |
| 5. #22609986 | C2 | semidirect |
| 6. #22608028 | C2 | semidirect |
| 7. C73×#1388 | C2 | semidirect |
| 16. #17988863 | C4 | semidirect |
| 17. #17988858 | C4 | semidirect |
| 186. #1388 | D73 | semidirect |
| 188. C73 | #13071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989005 | 2 |
| #22619652 | 2 |
| #22611668 | 2 |
| C2×#17988393 | 2 |
| #22609986 | 2 |
| #22608028 | 2 |
| C73×#1388 | 2 |
| #13071 | 73 |