Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
428 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22609977 | C2 | semidirect |
| 4. #22608051 | C2 | semidirect |
| 5. C73×#1812 | C2 | semidirect |
| 6. C2×#14556597 | C4 | semidirect |
| 13. #17988610 | C4 | semidirect |
| 15. #17988555 | C4 | semidirect |
| 17. C2×C8×Dic73 | C4 | semidirect |
| 189. #1812 | D73 | semidirect |
| 191. C73 | #12807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618641 | 2 |
| #22611594 | 2 |
| #22609977 | 2 |
| #22608051 | 2 |
| C73×#1812 | 2 |
| #12807 | 73 |