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. #23750278 | C2 | semidirect |
| 2. #23749940 | C2 | semidirect |
| 3. #23749902 | C2 | semidirect |
| 4. #23749862 | C2 | semidirect |
| 5. C4×D1192 | C2 | semidirect |
| 6. C8×D596 | C2 | semidirect |
| 7. #107×D149 | C2 | semidirect |
| 8. #500×C149 | C2 | semidirect |
| 55. D596 | D8 | semidirect |
| 69. C8×C149 | #41 | semidirect |
| 89. C149 | #3334 | semidirect |
| 92. #500 | D149 | semidirect |
| 159. C8 | #14558737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750278 | 2 |
| #23749940 | 2 |
| #23749902 | 2 |
| #23749862 | 2 |
| C4×D1192 | 2 |
| C8×D596 | 2 |
| #107×D149 | 2 |
| #500×C149 | 2 |
| #3334 | 149 |