Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
214 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 119 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. #22608067 | C2 | semidirect |
| 4. #22608066 | C2 | semidirect |
| 5. C73×#1398 | C2 | semidirect |
| 10. #17988420 | C4 | semidirect |
| 11. C32×D73 | C4 | semidirect |
| 78. #1398 | D73 | semidirect |
| 79. C73 | #13551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M64×D73 | 2 |
| #22611529 | 2 |
| #22608067 | 2 |
| #22608066 | 2 |
| C73×#1398 | 2 |
| #13551 | 73 |