Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
740 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×D4×Dic149 | C2 | semidirect |
| 3. C2×#18011873 | C2 | semidirect |
| 4. #23749527 | C2 | semidirect |
| 5. #23749502 | C2 | semidirect |
| 6. #23749501 | C2 | semidirect |
| 7. #23749490 | C2 | semidirect |
| 8. #23749471 | C2 | semidirect |
| 9. #390×C149 | C2 | semidirect |
| 14. #18011907 | C4 | semidirect |
| 33. C2×D596 | C2×C4 | semidirect |
| 36. C2×C22⋊D149 | C2×C4 | semidirect |
| 49. C4×Dic149 | C2×C4 | semidirect |
| 50. C4×Dic149 | D4 | semidirect |
| 54. C2×D4×C149 | C2×C4 | semidirect |
| 123. C149 | #2328 | semidirect |
| 129. #390 | D149 | semidirect |
| 164. C2×D4 | C4×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011907 | 2 |
| C2×D4×Dic149 | 2 |
| C2×#18011873 | 2 |
| #23749527 | 2 |
| #23749502 | 2 |
| #23749501 | 2 |
| #23749490 | 2 |
| #23749471 | 2 |
| #390×C149 | 2 |
| #2328 | 149 |