Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
290 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22611967 | C2 | semidirect |
| 2. #22611963 | C2 | semidirect |
| 3. #22609545 | C2 | semidirect |
| 4. #22608725 | C2 | semidirect |
| 5. #22608000 | C2 | semidirect |
| 6. #22607976 | C2 | semidirect |
| 7. C73×#1361 | C2 | semidirect |
| 55. D584 | D8 | semidirect |
| 104. #10596831 | D16 | semidirect |
| 134. #1361 | D73 | semidirect |
| 135. C73 | #12424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611967 | 2 |
| #22611963 | 2 |
| #22609545 | 2 |
| #22608725 | 2 |
| #22608000 | 2 |
| #22607976 | 2 |
| C73×#1361 | 2 |
| #12424 | 73 |