Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. #22609678 | C2 | semidirect |
| 3. #22609675 | C2 | semidirect |
| 4. #22607754 | C2 | semidirect |
| 7. C73×#1271 | C2 | semidirect |
| 198. #1271 | D73 | semidirect |
| 201. C73 | #7692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618299 | 2 |
| #22609678 | 2 |
| #22609675 | 2 |
| #22607754 | 2 |
| #22607751 | 2 |
| C73×#1271 | 2 |
| #7692 | 73 |