Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#18011932 | C2 | semidirect |
| 2. C2×#18011930 | C2 | semidirect |
| 3. #23750174 | C2 | semidirect |
| 4. #23750173 | C2 | semidirect |
| 5. #23750020 | C2 | semidirect |
| 6. #23750019 | C2 | semidirect |
| 7. #23750016 | C2 | semidirect |
| 8. #23750013 | C2 | semidirect |
| 9. #23750012 | C2 | semidirect |
| 10. #97×D149 | C2 | semidirect |
| 11. #496×C149 | C2 | semidirect |
| 64. C8×D149 | D4 | semidirect |
| 133. C149 | #3150 | semidirect |
| 144. #496 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011932 | 2 |
| C2×#18011930 | 2 |
| #23750174 | 2 |
| #23750173 | 2 |
| #23750020 | 2 |
| #23750019 | 2 |
| #23750016 | 2 |
| #23750013 | 2 |
| #23750012 | 2 |
| #97×D149 | 2 |
| #496×C149 | 2 |
| #3150 | 149 |