Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
376 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 376 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. #22611550 | C2 | semidirect |
| 3. #22609976 | C2 | semidirect |
| 4. #22607920 | C2 | semidirect |
| 5. #22607918 | C2 | semidirect |
| 6. #22607916 | C2 | semidirect |
| 7. C73×#1339 | C2 | semidirect |
| 8. C2×#14556610 | C4 | semidirect |
| 12. #17988846 | C4 | semidirect |
| 14. #17988837 | C4 | semidirect |
| 18. #106×D73 | C4 | semidirect |
| 190. #1339 | D73 | semidirect |
| 191. C73 | #11867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619591 | 2 |
| #22611550 | 2 |
| #22609976 | 2 |
| #22607920 | 2 |
| #22607918 | 2 |
| #22607916 | 2 |
| C73×#1339 | 2 |
| #11867 | 73 |