Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
290 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. #22612134 | C2 | semidirect |
| 4. #22611436 | C2 | semidirect |
| 5. #22607950 | C2 | semidirect |
| 7. C73×#1323 | C2 | semidirect |
| 149. #1323 | D73 | semidirect |
| 150. C73 | #12297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621392 | 2 |
| #22612134 | 2 |
| #22612112 | 2 |
| #22611436 | 2 |
| #22607950 | 2 |
| #22607947 | 2 |
| C73×#1323 | 2 |
| #12297 | 73 |