Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
354 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22610084 | C2 | semidirect |
| 3. #22608707 | C2 | semidirect |
| 6. #22607759 | C2 | semidirect |
| 7. C73×#1571 | C2 | semidirect |
| 133. #1571 | D73 | semidirect |
| 137. C73 | #10667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610762 | 2 |
| #22610084 | 2 |
| #22608707 | 2 |
| #22608331 | 2 |
| #22608329 | 2 |
| #22607759 | 2 |
| C73×#1571 | 2 |
| #10667 | 73 |