Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23750170 | C2 | semidirect |
| 2. #23750029 | C2 | semidirect |
| 3. #23750000 | C2 | semidirect |
| 4. #23749970 | C2 | semidirect |
| 5. #23749861 | C2 | semidirect |
| 6. #23749859 | C2 | semidirect |
| 7. D8×Dic149 | C2 | semidirect |
| 8. #23749707 | C2 | semidirect |
| 9. #23749705 | C2 | semidirect |
| 10. C2×C8×Dic149 | C2 | semidirect |
| 11. #466×C149 | C2 | semidirect |
| 82. C2×Dic149 | D8 | semidirect |
| 89. #11924746 | #41 | semidirect |
| 101. C8×C149 | #41 | semidirect |
| 127. C149 | #3169 | semidirect |
| 135. #466 | D149 | semidirect |
| 229. C8 | #14558735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750170 | 2 |
| #23750029 | 2 |
| #23750000 | 2 |
| #23749970 | 2 |
| #23749861 | 2 |
| #23749859 | 2 |
| D8×Dic149 | 2 |
| #23749707 | 2 |
| #23749705 | 2 |
| C2×C8×Dic149 | 2 |
| #466×C149 | 2 |
| #3169 | 149 |