Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
536 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#17988918 | C2 | semidirect |
| 4. #22610009 | C2 | semidirect |
| 5. #22608294 | C2 | semidirect |
| 7. C73×#1298 | C2 | semidirect |
| 200. #1298 | D73 | semidirect |
| 201. C73 | #9993 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620738 | 2 |
| C2×#17988906 | 2 |
| C2×#17988918 | 2 |
| #22610009 | 2 |
| #22608294 | 2 |
| #22608290 | 2 |
| C73×#1298 | 2 |
| #9993 | 73 |