Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23750159 | C2 | semidirect |
| 2. #23750027 | C2 | semidirect |
| 3. #23750009 | C2 | semidirect |
| 4. #23749980 | C2 | semidirect |
| 5. #23749883 | C2 | semidirect |
| 7. #23749871 | C2 | semidirect |
| 8. #23749738 | C2 | semidirect |
| 9. #23749733 | C2 | semidirect |
| 10. #23749727 | C2 | semidirect |
| 11. C4×M16×C149 | C2 | semidirect |
| 109. C149 | #3183 | semidirect |
| 121. C4×M16 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750159 | 2 |
| #23750027 | 2 |
| #23750009 | 2 |
| #23749980 | 2 |
| #23749883 | 2 |
| #23749878 | 2 |
| #23749871 | 2 |
| #23749738 | 2 |
| #23749733 | 2 |
| #23749727 | 2 |
| C4×M16×C149 | 2 |
| #3183 | 149 |