Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
686 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 686 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. #22612689 | C2 | semidirect |
| 4. #22608464 | C2 | semidirect |
| 5. #22607840 | C2 | semidirect |
| 6. #22607785 | C2 | semidirect |
| 27. #451×C73 | C4 | semidirect |
| 28. #450×C73 | C4 | semidirect |
| 274. C73 | #9524 | semidirect |
| 279. #451 | Dic73 | semidirect |
| 280. #450 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612689 | 2 |
| #22609875 | 2 |
| #22609849 | 2 |
| #22608464 | 2 |
| #22607840 | 2 |
| #22607785 | 2 |
| C73×#3007 | 2 |
| #9524 | 73 |