Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
364 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 364 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 |
|---|---|---|
| 1. #23750341 | C2 | semidirect |
| 2. #23749952 | C2 | semidirect |
| 3. #23749912 | C2 | semidirect |
| 4. #23749862 | C2 | semidirect |
| 5. C4×D1192 | C2 | semidirect |
| 6. C8×D596 | C2 | semidirect |
| 7. #23749662 | C2 | semidirect |
| 8. #500×C149 | C2 | semidirect |
| 87. C149 | #3341 | semidirect |
| 90. #500 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750341 | 2 |
| #23749952 | 2 |
| #23749912 | 2 |
| #23749862 | 2 |
| C4×D1192 | 2 |
| C8×D596 | 2 |
| #23749662 | 2 |
| #500×C149 | 2 |
| #3341 | 149 |