Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
602 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22610772 | C2 | semidirect |
| 3. #22610770 | C2 | semidirect |
| 4. #22608686 | C2 | semidirect |
| 5. #22608598 | C2 | semidirect |
| 6. #22608221 | C2 | semidirect |
| 7. C73×#1545 | C2 | semidirect |
| 142. #10596831 | #100 | semidirect |
| 174. #1545 | D73 | semidirect |
| 176. C73 | #9811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988963 | 2 |
| #22610772 | 2 |
| #22610770 | 2 |
| #22608686 | 2 |
| #22608598 | 2 |
| #22608221 | 2 |
| C73×#1545 | 2 |
| #9811 | 73 |