Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
554 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22621319 | C2 | semidirect |
| 2. #22621318 | C2 | semidirect |
| 4. #22610908 | C2 | semidirect |
| 5. #22610759 | C2 | semidirect |
| 6. #22607844 | C2 | semidirect |
| 7. C73×#1962 | C2 | semidirect |
| 224. #1962 | D73 | semidirect |
| 226. C73 | #10301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621319 | 2 |
| #22621318 | 2 |
| #22621309 | 2 |
| #22610908 | 2 |
| #22610759 | 2 |
| #22607844 | 2 |
| C73×#1962 | 2 |
| #10301 | 73 |