Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1226 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1226 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 3. #22607817 | C2 | semidirect |
| 4. #22607816 | C2 | semidirect |
| 5. C73×#1297 | C2 | semidirect |
| 7. C2×M16×D73 | C4 | semidirect |
| 11. #17988550 | C4 | semidirect |
| 17. #17988434 | C4 | semidirect |
| 18. #95×D73 | C4 | semidirect |
| 33. C2×#11924012 | C2×C4 | semidirect |
| 46. #14556498 | C2×C4 | semidirect |
| 48. C2×M16×C73 | C2×C4 | semidirect |
| 52. #95×C73 | C2×C4 | semidirect |
| 189. D73 | #1297 | direct (N × H) |
| 194. #1297 | D73 | direct (N × H) |
| 195. C73 | C2×#1297 | semidirect |
| 227. C2×M16 | C4×D73 | semidirect |
| 242. #95 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #407×D73 | 2 |
| C4×C22⋊C4×D73 | 2 |
| #22607817 | 2 |
| #22607816 | 2 |
| C73×#1297 | 2 |
| C2×#1297 | 73 |