Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
418 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 418 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. #22612155 | C2 | semidirect |
| 3. #22612079 | C2 | semidirect |
| 4. #22609330 | C2 | semidirect |
| 5. #22607978 | C2 | semidirect |
| 6. #22607893 | C2 | semidirect |
| 7. C73×D4⋊C16 | C2 | semidirect |
| 10. #17988992 | C22 | semidirect |
| 20. #17988340 | C22 | semidirect |
| 23. C4⋊C16×C73 | C22 | semidirect |
| 24. C4×C16×C73 | C22 | semidirect |
| 156. D4⋊C16 | D73 | semidirect |
| 157. C73 | #12372 | semidirect |
| 169. C4⋊C16 | C2×D73 | semidirect |
| 172. C4×C16 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D584 | 2 |
| #22612155 | 2 |
| #22612079 | 2 |
| #22609330 | 2 |
| #22607978 | 2 |
| #22607893 | 2 |
| C73×D4⋊C16 | 2 |
| #12372 | 73 |