Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#18011941 | C2 | semidirect |
| 2. C2×#18011898 | C2 | semidirect |
| 3. #23749803 | C2 | direct (N × H) |
| 4. C2×#18011838 | C2 | semidirect |
| 5. C2×#18011828 | C2 | semidirect |
| 7. C22×Dic298 | C22 | semidirect |
| 9. #18011941 | C22 | semidirect |
| 12. C2×#14558720 | C22 | semidirect |
| 14. #18011898 | C22 | semidirect |
| 16. C2×C4×Dic149 | C22 | semidirect |
| 17. #18011838 | C22 | semidirect |
| 18. #18011828 | C22 | semidirect |
| 30. C2×Dic298 | C23 | semidirect |
| 36. #14558720 | C23 | semidirect |
| 40. C4×Dic149 | C23 | semidirect |
| 117. C2×C149 | #455 | semidirect |
| 119. C149 | C2×#455 | semidirect |
| 237. C2 | #23749803 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011941 | 2 |
| C2×#18011898 | 2 |
| #23749803 | 2 |
| C2×#18011838 | 2 |
| C2×#18011828 | 2 |
| C2×H(5,𝔽2)×C149 | 2 |
| C2×#455 | 149 |