Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
300 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. #23750588 | C2 | semidirect |
| 4. C2×C8×#10597010 | C2 | semidirect |
| 5. #23750500 | C2 | semidirect |
| 6. #23750497 | C2 | semidirect |
| 12. #18011976 | C4 | semidirect |
| 13. #18011975 | C4 | semidirect |
| 14. #18011974 | C4 | semidirect |
| 15. #18011973 | C4 | semidirect |
| 22. #18011919 | C4 | semidirect |
| 23. #18011918 | C4 | semidirect |
| 25. #18011917 | C4 | semidirect |
| 30. #131×C149 | C4 | semidirect |
| 127. C149 | #1764 | semidirect |
| 142. #131 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D149⋊#104 | 2 |
| #23750615 | 2 |
| #23750588 | 2 |
| C2×C8×#10597010 | 2 |
| #23750500 | 2 |
| #23750497 | 2 |
| #131×D149 | 2 |
| #1764 | 149 |