Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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. #23749967 | C2 | direct (N × H) |
| 4. C2×#18011845 | C2 | semidirect |
| 5. C2×#18011843 | C2 | semidirect |
| 6. C2×#18011836 | C2 | semidirect |
| 7. C2×#18011836 | C2 | semidirect |
| 21. #18011845 | C22 | semidirect |
| 22. #18011843 | C22 | semidirect |
| 23. #18011836 | C22 | semidirect |
| 24. #18011836 | C22 | semidirect |
| 102. C2×C149 | #485 | semidirect |
| 106. C149 | C2×#485 | semidirect |
| 209. C2 | #23749967 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011890 | 2 |
| C2×#18011870 | 2 |
| #23749967 | 2 |
| C2×#18011845 | 2 |
| C2×#18011843 | 2 |
| C2×#18011836 | 2 |
| C2×C22⋊C8×C149 | 2 |
| C2×#485 | 149 |