Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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. Q8×D596 | C2 | semidirect |
| 3. #23749977 | C2 | semidirect |
| 4. #23749957 | C2 | semidirect |
| 5. #23749855 | C2 | semidirect |
| 6. #23749831 | C2 | semidirect |
| 7. #23749765 | C2 | semidirect |
| 8. C4×#14558723 | C2 | semidirect |
| 9. #23749690 | C2 | semidirect |
| 10. #103×D149 | C2 | semidirect |
| 11. #475×C149 | C2 | semidirect |
| 85. D596 | SD16 | semidirect |
| 98. Q8×C149 | #41 | semidirect |
| 128. C149 | #3298 | semidirect |
| 134. #475 | D149 | semidirect |
| 213. Q8 | #14558737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D596 | 2 |
| #23750278 | 2 |
| #23749977 | 2 |
| #23749957 | 2 |
| #23749855 | 2 |
| #23749831 | 2 |
| #23749765 | 2 |
| C4×#14558723 | 2 |
| #23749690 | 2 |
| #103×D149 | 2 |
| #475×C149 | 2 |
| #3298 | 149 |