Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
302 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 81 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. M64×D73 | C2 | semidirect |
| 3. #367×D73 | C2 | semidirect |
| 4. #22608119 | C2 | semidirect |
| 5. #22608118 | C2 | semidirect |
| 6. #22608117 | C2 | semidirect |
| 7. C73×#1418 | C2 | semidirect |
| 9. #17989020 | C4 | semidirect |
| 13. #17989016 | C4 | semidirect |
| 14. Q32×D73 | C4 | semidirect |
| 16. D16×D73 | C4 | semidirect |
| 19. #17988421 | C22 | semidirect |
| 22. #17988415 | C22 | semidirect |
| 25. M64×C73 | C22 | semidirect |
| 26. #367×C73 | C22 | semidirect |
| 38. Dic584 | C2×C4 | semidirect |
| 43. D1168 | C2×C4 | semidirect |
| 54. Q32×C73 | C2×C4 | semidirect |
| 56. D16×C73 | C2×C4 | semidirect |
| 146. D73 | #1418 | direct (N × H) |
| 153. #1418 | D73 | direct (N × H) |
| 154. C73 | C2×#1418 | semidirect |
| 169. M64 | C2×D73 | semidirect |
| 173. #367 | C2×D73 | semidirect |
| 188. Q32 | C4×D73 | semidirect |
| 195. D16 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #508×D73 | 2 |
| M64×D73 | 2 |
| #367×D73 | 2 |
| #22608119 | 2 |
| #22608118 | 2 |
| #22608117 | 2 |
| C73×#1418 | 2 |
| C2×#1418 | 73 |