Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
458 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 1. D8×D292 | C2 | semidirect |
| 2. #22612181 | C2 | semidirect |
| 3. #22611966 | C2 | semidirect |
| 4. #22609287 | C2 | semidirect |
| 5. #22607976 | C2 | semidirect |
| 6. #22607887 | C2 | semidirect |
| 7. C73×#1331 | C2 | semidirect |
| 13. #17988964 | C22 | semidirect |
| 19. C4⋊#11924003 | C22 | semidirect |
| 23. C4×C16×C73 | C22 | semidirect |
| 24. #335×C73 | C22 | semidirect |
| 89. D8×C73 | D8 | semidirect |
| 126. D292 | D16 | semidirect |
| 168. #1331 | D73 | semidirect |
| 170. C73 | #12316 | semidirect |
| 185. C4×C16 | C2×D73 | semidirect |
| 186. #335 | C2×D73 | semidirect |
| 245. D8 | D584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D292 | 2 |
| #22612181 | 2 |
| #22611966 | 2 |
| #22609287 | 2 |
| #22607976 | 2 |
| #22607887 | 2 |
| C73×#1331 | 2 |
| #12316 | 73 |