Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
592 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 592 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 |
|---|---|---|
| 1. #22621309 | C2 | semidirect |
| 2. #22610760 | C2 | semidirect |
| 3. #22610758 | C2 | semidirect |
| 4. #22607844 | C2 | semidirect |
| 5. C73×#3253 | C2 | semidirect |
| 146. #3253 | D73 | semidirect |
| 150. C73 | #10300 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621309 | 2 |
| #22610760 | 2 |
| #22610758 | 2 |
| #22607844 | 2 |
| C73×#3253 | 2 |
| #10300 | 73 |