Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
386 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22610105 | C2 | semidirect |
| 3. #22608651 | C2 | semidirect |
| 4. #22608543 | C2 | semidirect |
| 5. #22608542 | C2 | semidirect |
| 6. #22607841 | C2 | semidirect |
| 7. C73×#1557 | C2 | semidirect |
| 166. #1557 | D73 | semidirect |
| 170. C73 | #10524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621309 | 2 |
| #22610105 | 2 |
| #22608651 | 2 |
| #22608543 | 2 |
| #22608542 | 2 |
| #22607841 | 2 |
| C73×#1557 | 2 |
| #10524 | 73 |