Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
398 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 1. #22615580 | C2 | semidirect |
| 5. #22607825 | C2 | semidirect |
| 6. #22607788 | C2 | semidirect |
| 7. C73×#1288 | C2 | semidirect |
| 29. #14556591 | Q8 | semidirect |
| 30. #14556588 | Q8 | semidirect |
| 187. #1288 | D73 | semidirect |
| 189. C73 | #10378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22615580 | 2 |
| #22610850 | 2 |
| #22608477 | 2 |
| #22608440 | 2 |
| #22607825 | 2 |
| #22607788 | 2 |
| C73×#1288 | 2 |
| #10378 | 73 |