Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. Q8×Dic298 | C2 | semidirect |
| 3. #23749986 | C2 | semidirect |
| 5. #23749920 | C2 | semidirect |
| 6. #23749904 | C2 | semidirect |
| 7. #23749849 | C2 | semidirect |
| 9. #23749755 | C2 | semidirect |
| 10. #23749728 | C2 | semidirect |
| 11. C4×Q16×C149 | C2 | semidirect |
| 118. C149 | #3375 | semidirect |
| 130. C4×Q16 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750360 | 2 |
| Q8×Dic298 | 2 |
| #23749986 | 2 |
| #23749972 | 2 |
| #23749920 | 2 |
| #23749904 | 2 |
| #23749849 | 2 |
| #23749825 | 2 |
| #23749755 | 2 |
| #23749728 | 2 |
| C4×Q16×C149 | 2 |
| #3375 | 149 |