Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
424 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #22610217 | C2 | semidirect |
| 5. #22608052 | C2 | semidirect |
| 6. #22608051 | C2 | semidirect |
| 7. C73×#1868 | C2 | semidirect |
| 20. #17988381 | C4 | semidirect |
| 21. #17988379 | C4 | semidirect |
| 194. #1868 | D73 | semidirect |
| 197. C73 | #12968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618995 | 2 |
| #22611594 | 2 |
| #22610314 | 2 |
| #22610217 | 2 |
| #22608052 | 2 |
| #22608051 | 2 |
| C73×#1868 | 2 |
| #12968 | 73 |