Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 123 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×#18011910 | C2 | semidirect |
| 3. #23750022 | C2 | semidirect |
| 4. #23749970 | C2 | semidirect |
| 5. #23749944 | C2 | semidirect |
| 6. #23749943 | C2 | semidirect |
| 7. #23749941 | C2 | semidirect |
| 8. #23749914 | C2 | semidirect |
| 9. #23749913 | C2 | semidirect |
| 10. #23749675 | C2 | semidirect |
| 11. #481×C149 | C2 | semidirect |
| 137. C149 | #3227 | semidirect |
| 146. #481 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750170 | 2 |
| C2×#18011910 | 2 |
| #23750022 | 2 |
| #23749970 | 2 |
| #23749944 | 2 |
| #23749943 | 2 |
| #23749941 | 2 |
| #23749914 | 2 |
| #23749913 | 2 |
| #23749675 | 2 |
| #481×C149 | 2 |
| #3227 | 149 |