Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
330 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 4. #22607828 | C2 | semidirect |
| 5. #22607791 | C2 | semidirect |
| 6. #22607790 | C2 | semidirect |
| 7. C73×#1571 | C2 | semidirect |
| 149. #1571 | D73 | semidirect |
| 154. C73 | #10638 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22609942 | 2 |
| #22609920 | 2 |
| #22608323 | 2 |
| #22607828 | 2 |
| #22607791 | 2 |
| #22607790 | 2 |
| C73×#1571 | 2 |
| #10638 | 73 |