Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
434 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#17988402 | C2 | semidirect |
| 5. #22611650 | C2 | semidirect |
| 6. #22611536 | C2 | semidirect |
| 7. C73×#1833 | C2 | semidirect |
| 15. #17988971 | C4 | semidirect |
| 16. #17988967 | C4 | semidirect |
| 175. #1833 | D73 | semidirect |
| 176. C73 | #13216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620425 | 2 |
| C2×#17988402 | 2 |
| #22611666 | 2 |
| #22611658 | 2 |
| #22611650 | 2 |
| #22611536 | 2 |
| C73×#1833 | 2 |
| #13216 | 73 |