Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
424 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 424 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. #22612156 | C2 | semidirect |
| 3. #22612065 | C2 | semidirect |
| 4. #22607976 | C2 | semidirect |
| 5. #22607891 | C2 | semidirect |
| 6. D4⋊#11924003 | C2 | semidirect |
| 7. C73×#1673 | C2 | semidirect |
| 16. C4⋊#11924003 | C22 | semidirect |
| 19. C4×#11924003 | C22 | semidirect |
| 20. #500×C73 | C22 | semidirect |
| 23. #335×C73 | C22 | semidirect |
| 71. D584 | SD16 | semidirect |
| 155. #1673 | D73 | semidirect |
| 159. C73 | #12368 | semidirect |
| 162. #500 | C2×D73 | semidirect |
| 175. #335 | 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 |
| #22612156 | 2 |
| #22612065 | 2 |
| #22607976 | 2 |
| #22607891 | 2 |
| D4⋊#11924003 | 2 |
| C73×#1673 | 2 |
| #12368 | 73 |