Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
424 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22612065 | C2 | semidirect |
| 3. #22609317 | C2 | semidirect |
| 4. #22607977 | C2 | semidirect |
| 5. #22607893 | C2 | semidirect |
| 6. #22607887 | C2 | semidirect |
| 7. C73×#2240 | C2 | semidirect |
| 17. C4⋊#11924003 | C22 | semidirect |
| 19. #17988340 | C22 | semidirect |
| 21. #500×C73 | C22 | semidirect |
| 24. C4×C16×C73 | C22 | semidirect |
| 67. D584 | SD16 | semidirect |
| 153. #2240 | D73 | semidirect |
| 159. C73 | #12368 | semidirect |
| 162. #500 | C2×D73 | semidirect |
| 174. C4×C16 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621606 | 2 |
| #22612065 | 2 |
| #22609317 | 2 |
| #22607977 | 2 |
| #22607893 | 2 |
| #22607887 | 2 |
| C73×#2240 | 2 |
| #12368 | 73 |