Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
372 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22612168 | C2 | semidirect |
| 3. #22612078 | C2 | semidirect |
| 4. #22609445 | C2 | semidirect |
| 5. #22607973 | C2 | semidirect |
| 6. #22607890 | C2 | semidirect |
| 7. C73×#1333 | C2 | semidirect |
| 10. #17988992 | C22 | semidirect |
| 19. C4⋊#11924003 | C22 | semidirect |
| 25. #346×C73 | C22 | semidirect |
| 26. #334×C73 | C22 | semidirect |
| 99. D8×C73 | SD16 | semidirect |
| 172. #1333 | D73 | semidirect |
| 174. C73 | #12378 | semidirect |
| 191. #346 | C2×D73 | semidirect |
| 192. #334 | C2×D73 | semidirect |
| 253. D8 | #11924017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621541 | 2 |
| #22612168 | 2 |
| #22612078 | 2 |
| #22609445 | 2 |
| #22607973 | 2 |
| #22607890 | 2 |
| C73×#1333 | 2 |
| #12378 | 73 |