Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
434 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#17988403 | C2 | semidirect |
| 4. #22611651 | C2 | semidirect |
| 5. #22611536 | C2 | semidirect |
| 6. #22610055 | C2 | semidirect |
| 24. #495×C73 | C4 | semidirect |
| 25. #494×C73 | C4 | semidirect |
| 176. C73 | #13216 | semidirect |
| 184. #495 | Dic73 | semidirect |
| 185. #494 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988403 | 2 |
| #22611667 | 2 |
| #22611659 | 2 |
| #22611651 | 2 |
| #22611536 | 2 |
| #22610055 | 2 |
| C73×#3156 | 2 |
| #13216 | 73 |