Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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. #41×Dic149 | C2 | semidirect |
| 4. #23749845 | C2 | semidirect |
| 5. #23749838 | C2 | semidirect |
| 6. #23749648 | C2 | semidirect |
| 7. #23749635 | C2 | semidirect |
| 8. #23749630 | C2 | semidirect |
| 12. C2×#14558726 | C22 | semidirect |
| 13. C2×#14558724 | C22 | semidirect |
| 18. Q8×Dic149 | C22 | semidirect |
| 20. D4×Dic149 | C22 | semidirect |
| 26. #18011840 | C22 | semidirect |
| 27. #18011836 | C22 | semidirect |
| 125. C149 | #3040 | semidirect |
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 |
| #41×Dic149 | 2 |
| #23749845 | 2 |
| #23749838 | 2 |
| #23749648 | 2 |
| #23749635 | 2 |
| #23749630 | 2 |
| C2×AGL(1,ℤ/8)×C149 | 2 |
| #3040 | 149 |