Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
460 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 460 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. #22610097 | C2 | semidirect |
| 4. C2×#17988329 | C2 | semidirect |
| 6. #22607813 | C2 | semidirect |
| 7. C73×#1992 | C2 | semidirect |
| 211. #1992 | D73 | semidirect |
| 217. C73 | #10427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22617981 | 2 |
| #22610745 | 2 |
| #22610097 | 2 |
| C2×#17988329 | 2 |
| C2×#17988326 | 2 |
| #22607813 | 2 |
| C73×#1992 | 2 |
| #10427 | 73 |