Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1056 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22621059 | C2 | semidirect |
| 3. #22609074 | C2 | semidirect |
| 4. #22609045 | C2 | semidirect |
| 5. #22608593 | C2 | semidirect |
| 6. #22608349 | C2 | semidirect |
| 7. C73×#3152 | C2 | semidirect |
| 19. #17988874 | C22 | semidirect |
| 20. #17988640 | C22 | semidirect |
| 21. #17988336 | C22 | semidirect |
| 23. #17988316 | C22 | semidirect |
| 26. C2×C4⋊Q8×C73 | C22 | semidirect |
| 28. #494×C73 | C22 | semidirect |
| 30. C4×M16×C73 | C22 | semidirect |
| 174. #3152 | D73 | semidirect |
| 179. C73 | #18715 | semidirect |
| 190. C2×C4⋊Q8 | C2×D73 | semidirect |
| 193. #494 | C2×D73 | semidirect |
| 199. C4×M16 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22624336 | 2 |
| #22621059 | 2 |
| #22609074 | 2 |
| #22609045 | 2 |
| #22608593 | 2 |
| #22608349 | 2 |
| C73×#3152 | 2 |
| #18715 | 73 |