Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
346 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22612099 | C2 | semidirect |
| 3. #22609533 | C2 | semidirect |
| 4. #22607971 | C2 | semidirect |
| 5. #22607904 | C2 | semidirect |
| 6. #22607903 | C2 | semidirect |
| 7. C73×#2230 | C2 | semidirect |
| 19. #17988408 | C22 | semidirect |
| 21. C8×#10596831 | C22 | semidirect |
| 22. #498×C73 | C22 | semidirect |
| 25. #364×C73 | C22 | semidirect |
| 168. #2230 | D73 | semidirect |
| 173. C73 | #12365 | semidirect |
| 176. #498 | C2×D73 | semidirect |
| 189. #364 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621725 | 2 |
| #22612099 | 2 |
| #22609533 | 2 |
| #22607971 | 2 |
| #22607904 | 2 |
| #22607903 | 2 |
| C73×#2230 | 2 |
| #12365 | 73 |