Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22610104 | C2 | semidirect |
| 5. #22608042 | C2 | semidirect |
| 6. #22608010 | C2 | semidirect |
| 7. C73×#1388 | C2 | semidirect |
| 143. #1388 | D73 | semidirect |
| 145. C73 | #13486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611681 | 2 |
| #22611678 | 2 |
| #22610822 | 2 |
| #22610104 | 2 |
| #22608042 | 2 |
| #22608010 | 2 |
| C73×#1388 | 2 |
| #13486 | 73 |