Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 88 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. #23750591 | C2 | semidirect |
| 4. #23750584 | C2 | semidirect |
| 5. #23750500 | C2 | semidirect |
| 6. #23750496 | C2 | semidirect |
| 8. #18011999 | C4 | semidirect |
| 10. #18011998 | C4 | semidirect |
| 17. #18011974 | C4 | semidirect |
| 18. #18011973 | C4 | semidirect |
| 25. #18011839 | C4 | semidirect |
| 26. #18011838 | C4 | semidirect |
| 27. #18011837 | C4 | semidirect |
| 28. #104×C149 | C4 | semidirect |
| 120. C149 | #1765 | semidirect |
| 144. #104 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D149⋊#131 | 2 |
| #23750615 | 2 |
| #23750591 | 2 |
| #23750584 | 2 |
| #23750500 | 2 |
| #23750496 | 2 |
| #104×D149 | 2 |
| #1765 | 149 |