Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 2. #22610707 | C2 | semidirect |
| 3. #22608684 | C2 | semidirect |
| 6. #22607805 | C2 | semidirect |
| 7. C73×#1571 | C2 | semidirect |
| 160. #1571 | D73 | semidirect |
| 165. C73 | #10603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610770 | 2 |
| #22610707 | 2 |
| #22608684 | 2 |
| #22608598 | 2 |
| C2×#17988330 | 2 |
| #22607805 | 2 |
| C73×#1571 | 2 |
| #10603 | 73 |