Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
388 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 82 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. #22626287 | C2 | semidirect |
| 4. #22626041 | C2 | semidirect |
| 5. #22625013 | C2 | semidirect |
| 6. #22624977 | C2 | semidirect |
| 27. #17988398 | C4 | semidirect |
| 28. #17988397 | C4 | semidirect |
| 29. #17988396 | C4 | semidirect |
| 30. #360×C73 | C4 | semidirect |
| 200. C73 | #12944 | semidirect |
| 220. #360 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D73⋊#444 | 2 |
| #22626287 | 2 |
| #22626245 | 2 |
| #22626041 | 2 |
| #22625013 | 2 |
| #22624977 | 2 |
| #22611665 | 2 |
| #12944 | 73 |