Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
498 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22621052 | C2 | semidirect |
| 3. #22610921 | C2 | semidirect |
| 4. #22608522 | C2 | semidirect |
| 5. #22608348 | C2 | semidirect |
| 6. #22607821 | C2 | semidirect |
| 7. C73×#3141 | C2 | semidirect |
| 187. #3141 | D73 | semidirect |
| 192. C73 | #10110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621309 | 2 |
| #22621052 | 2 |
| #22610921 | 2 |
| #22608522 | 2 |
| #22608348 | 2 |
| #22607821 | 2 |
| C73×#3141 | 2 |
| #10110 | 73 |