Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
590 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22609998 | C2 | semidirect |
| 3. #22609692 | C2 | semidirect |
| 4. #22607754 | C2 | semidirect |
| 5. #22607751 | C2 | semidirect |
| 6. #22607751 | C2 | semidirect |
| 7. C73×#1271 | C2 | semidirect |
| 232. #1271 | D73 | semidirect |
| 235. C73 | #7620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612439 | 2 |
| #22609998 | 2 |
| #22609692 | 2 |
| #22607754 | 2 |
| #22607751 | 2 |
| C73×#1271 | 2 |
| #7620 | 73 |