Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#18011903 | C2 | semidirect |
| 3. #23749994 | C2 | semidirect |
| 4. #23749990 | C2 | semidirect |
| 5. #23749980 | C2 | semidirect |
| 6. #23749627 | C2 | semidirect |
| 7. C4×M16×C149 | C2 | semidirect |
| 77. C149 | #3142 | semidirect |
| 85. C4×M16 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750175 | 2 |
| C2×#18011903 | 2 |
| #23749994 | 2 |
| #23749990 | 2 |
| #23749980 | 2 |
| #23749627 | 2 |
| C4×M16×C149 | 2 |
| #3142 | 149 |