Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
408 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23750175 | C2 | semidirect |
| 2. #23750159 | C2 | semidirect |
| 3. #23750034 | C2 | semidirect |
| 4. #23750014 | C2 | semidirect |
| 5. #23749990 | C2 | semidirect |
| 6. #23749985 | C2 | semidirect |
| 7. #23749878 | C2 | semidirect |
| 8. #23749871 | C2 | semidirect |
| 9. C4×#14558725 | C2 | semidirect |
| 10. C4×D1192 | C2 | semidirect |
| 11. C4×M16×C149 | C2 | semidirect |
| 110. C8×C149 | #41 | semidirect |
| 137. C149 | #3171 | semidirect |
| 149. C4×M16 | D149 | semidirect |
| 248. C8 | #14558736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750175 | 2 |
| #23750159 | 2 |
| #23750034 | 2 |
| #23750014 | 2 |
| #23749990 | 2 |
| #23749985 | 2 |
| #23749878 | 2 |
| #23749871 | 2 |
| C4×#14558725 | 2 |
| C4×D1192 | 2 |
| C4×M16×C149 | 2 |
| #3171 | 149 |