Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22610919 | C2 | semidirect |
| 4. #22608649 | C2 | semidirect |
| 6. #22607804 | C2 | semidirect |
| 7. C73×#1307 | C2 | semidirect |
| 184. #1307 | D73 | semidirect |
| 186. C73 | #9338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621154 | 2 |
| #22619098 | 2 |
| #22610919 | 2 |
| #22608649 | 2 |
| #22608539 | 2 |
| #22607804 | 2 |
| C73×#1307 | 2 |
| #9338 | 73 |