Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
440 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 84 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. #22624924 | C2 | semidirect |
| 4. #22624923 | C2 | semidirect |
| 172. C73 | #11712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626159 | 2 |
| C2×#17989463 | 2 |
| #22624924 | 2 |
| #22624923 | 2 |
| #467×D73 | 2 |
| #11712 | 73 |