Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 3. #23749976 | C2 | semidirect |
| 4. #23749962 | C2 | semidirect |
| 5. #23749920 | C2 | semidirect |
| 6. #23749865 | C2 | semidirect |
| 7. #23749835 | C2 | semidirect |
| 8. #23749779 | C2 | semidirect |
| 10. #103×D149 | C2 | semidirect |
| 11. C4×Q16×C149 | C2 | semidirect |
| 81. D596 | Q16 | semidirect |
| 122. C149 | #3299 | semidirect |
| 132. C4×Q16 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750335 | 2 |
| Q8×D596 | 2 |
| #23749976 | 2 |
| #23749962 | 2 |
| #23749920 | 2 |
| #23749865 | 2 |
| #23749835 | 2 |
| #23749779 | 2 |
| C8×D596 | 2 |
| #103×D149 | 2 |
| C4×Q16×C149 | 2 |
| #3299 | 149 |