Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
340 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 340 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. #23749968 | C2 | semidirect |
| 3. #23749907 | C2 | semidirect |
| 4. #23749867 | C2 | semidirect |
| 5. C4×Dic596 | C2 | semidirect |
| 7. #23749662 | C2 | semidirect |
| 8. #500×C149 | C2 | semidirect |
| 82. C149 | #3342 | semidirect |
| 85. #500 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750349 | 2 |
| #23749968 | 2 |
| #23749907 | 2 |
| #23749867 | 2 |
| C4×Dic596 | 2 |
| C8×D596 | 2 |
| #23749662 | 2 |
| #500×C149 | 2 |
| #3342 | 149 |