Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
456 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22619007 | C2 | semidirect |
| 2. #22608439 | C2 | semidirect |
| 3. #22608439 | C2 | semidirect |
| 4. #22608400 | C2 | semidirect |
| 5. #22607793 | C2 | semidirect |
| 6. #22607759 | C2 | semidirect |
| 22. #493×C73 | C4 | semidirect |
| 23. #492×C73 | C4 | semidirect |
| 24. #487×C73 | C4 | semidirect |
| 25. #486×C73 | C4 | semidirect |
| 186. C73 | #9281 | semidirect |
| 189. #493 | Dic73 | semidirect |
| 190. #492 | Dic73 | semidirect |
| 191. #487 | Dic73 | semidirect |
| 192. #486 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619007 | 2 |
| #22608439 | 2 |
| #22608400 | 2 |
| #22607793 | 2 |
| #22607759 | 2 |
| C73×#3207 | 2 |
| #9281 | 73 |