Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #22608615 | C2 | semidirect |
| 4. #22608613 | C2 | semidirect |
| 6. #22607828 | C2 | semidirect |
| 7. C73×#1570 | C2 | semidirect |
| 164. #1570 | D73 | semidirect |
| 169. C73 | #10448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988868 | 2 |
| #22609920 | 2 |
| #22608615 | 2 |
| #22608613 | 2 |
| #22608321 | 2 |
| #22607828 | 2 |
| C73×#1570 | 2 |
| #10448 | 73 |