Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
416 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22611596 | C2 | semidirect |
| 3. #22608095 | C2 | semidirect |
| 4. #22608093 | C2 | semidirect |
| 5. C73×#2126 | C2 | semidirect |
| 8. #17989137 | C4 | semidirect |
| 11. #17988966 | C4 | semidirect |
| 13. #17988961 | C4 | semidirect |
| 16. C2×C4×#10596831 | C4 | semidirect |
| 176. #2126 | D73 | semidirect |
| 179. C73 | #13583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620357 | 2 |
| #22611596 | 2 |
| #22608095 | 2 |
| #22608093 | 2 |
| C73×#2126 | 2 |
| #13583 | 73 |