Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
768 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22620679 | C2 | semidirect |
| 2. #22619183 | C2 | semidirect |
| 3. #22609843 | C2 | semidirect |
| 4. #22608292 | C2 | semidirect |
| 5. #22608291 | C2 | semidirect |
| 6. #22607807 | C2 | semidirect |
| 7. C73×#3006 | C2 | semidirect |
| 258. #3006 | D73 | semidirect |
| 263. C73 | #9974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620679 | 2 |
| #22619183 | 2 |
| #22609843 | 2 |
| #22608292 | 2 |
| #22608291 | 2 |
| #22607807 | 2 |
| C73×#3006 | 2 |
| #9974 | 73 |