Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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. #23749525 | C2 | semidirect |
| 3. #23749519 | C2 | semidirect |
| 4. #23749513 | C2 | semidirect |
| 5. #23749501 | C2 | semidirect |
| 6. #23749481 | C2 | semidirect |
| 7. #379×C149 | C2 | semidirect |
| 9. C22×C4×D149 | C22 | semidirect |
| 10. #18011880 | C4 | semidirect |
| 11. C2×#14558715 | C22 | semidirect |
| 15. C2×#14558713 | C22 | semidirect |
| 16. C2×C4×Dic149 | C22 | semidirect |
| 17. #18011818 | C22 | semidirect |
| 18. #18011818 | C22 | semidirect |
| 33. C22⋊Dic149 | C2×C4 | semidirect |
| 38. C24×C149 | C2×C4 | semidirect |
| 95. C149 | #2375 | semidirect |
| 103. #379 | D149 | semidirect |
| 121. C24 | C4×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011880 | 2 |
| #23749525 | 2 |
| #23749519 | 2 |
| #23749513 | 2 |
| #23749501 | 2 |
| #23749481 | 2 |
| #379×C149 | 2 |
| #2375 | 149 |