Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1506 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 1506 conjugacy classes of subgroups — too many to draw. Only its 242 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 |
|---|---|---|
| 1. C22×#14556679 | C2 | semidirect |
| 2. C2×#17989614 | C2 | semidirect |
| 3. #22625909 | C2 | semidirect |
| 4. #22625879 | C2 | semidirect |
| 5. #22625756 | C2 | semidirect |
| 6. #22625665 | C2 | semidirect |
| 30. C2×#11924036 | D4 | semidirect |
| 95. C23×C73 | #131 | semidirect |
| 113. C2×Dic73 | #131 | semidirect |
| 154. C73 | #21442 | semidirect |
| 247. C23 | #14556679 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556679 | 2 |
| C2×#17989614 | 2 |
| #22625909 | 2 |
| #22625879 | 2 |
| #22625756 | 2 |
| #22625665 | 2 |
| #22613148 | 2 |
| #21442 | 73 |