Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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. #23750640 | C2 | semidirect |
| 4. M16×#10597010 | C2 | semidirect |
| 5. #23750508 | C2 | semidirect |
| 6. #23750497 | C2 | semidirect |
| 23. #18011829 | C4 | semidirect |
| 24. #18011829 | C4 | semidirect |
| 25. #18011828 | C4 | semidirect |
| 26. #100×C149 | C4 | semidirect |
| 105. C149 | #1932 | semidirect |
| 130. #100 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750640 | 2 |
| #23750623 | 2 |
| C2×#18011975 | 2 |
| M16×#10597010 | 2 |
| #23750508 | 2 |
| #23750497 | 2 |
| #23749606 | 2 |
| #1932 | 149 |