Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
464 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22618991 | C2 | semidirect |
| 3. #22608488 | C2 | semidirect |
| 4. #22608460 | C2 | semidirect |
| 5. #22607840 | C2 | semidirect |
| 6. #22607808 | C2 | semidirect |
| 7. C73×#1471 | C2 | semidirect |
| 9. #17988917 | C4 | semidirect |
| 11. #17988900 | C4 | semidirect |
| 14. #17988738 | C4 | semidirect |
| 16. #17988721 | C4 | semidirect |
| 230. #1471 | D73 | semidirect |
| 233. C73 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620745 | 2 |
| #22618991 | 2 |
| #22608488 | 2 |
| #22608460 | 2 |
| #22607840 | 2 |
| #22607808 | 2 |
| C73×#1471 | 2 |
| #9332 | 73 |