Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. #23750182 | C2 | semidirect |
| 3. #23749985 | C2 | semidirect |
| 4. #23749980 | C2 | semidirect |
| 5. #23749635 | C2 | semidirect |
| 7. C4×M16×C149 | C2 | semidirect |
| 10. #18011911 | C22 | semidirect |
| 11. #18011903 | C22 | semidirect |
| 19. #18011836 | C22 | semidirect |
| 23. #97×C149 | C22 | semidirect |
| 24. C4×C8×C149 | C22 | semidirect |
| 83. C149 | #3140 | semidirect |
| 91. C4×M16 | D149 | semidirect |
| 107. #97 | C2×D149 | semidirect |
| 108. C4×C8 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750182 | 2 |
| C2×#18011899 | 2 |
| #23749985 | 2 |
| #23749980 | 2 |
| #23749635 | 2 |
| #23749631 | 2 |
| C4×M16×C149 | 2 |
| #3140 | 149 |