Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
574 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 574 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 |
|---|---|---|
| 1. #22621052 | C2 | semidirect |
| 3. #22610752 | C2 | semidirect |
| 4. #22608492 | C2 | semidirect |
| 5. #22608491 | C2 | semidirect |
| 6. #22607775 | C2 | semidirect |
| 7. C73×#3226 | C2 | semidirect |
| 199. #3226 | D73 | semidirect |
| 205. C73 | #10225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621052 | 2 |
| #22620376 | 2 |
| #22610752 | 2 |
| #22608492 | 2 |
| #22608491 | 2 |
| #22607775 | 2 |
| C73×#3226 | 2 |
| #10225 | 73 |