Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
772 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 202 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×D149⋊M16 | C2 | semidirect |
| 2. C2×#18011990 | C2 | semidirect |
| 3. #23750623 | C2 | direct (N × H) |
| 4. C2×#18011975 | C2 | semidirect |
| 6. C2×#14558746 | C22 | semidirect |
| 8. D149⋊M16 | C22 | semidirect |
| 12. #18011990 | C22 | semidirect |
| 15. C2×C4×#10597010 | C22 | semidirect |
| 16. #18011975 | C22 | semidirect |
| 21. C2×#14558735 | C4 | semidirect |
| 22. C2×#14558735 | C4 | semidirect |
| 25. C22×Dic298 | C4 | semidirect |
| 29. C22×D4×C149 | C4 | semidirect |
| 32. #14558746 | C23 | semidirect |
| 39. C4×#10597010 | C23 | semidirect |
| 49. #14558735 | C2×C4 | semidirect |
| 54. C2×Dic298 | C2×C4 | semidirect |
| 77. C2×D4×C149 | C2×C4 | semidirect |
| 146. C2×C149 | #421 | semidirect |
| 151. C149 | C2×#421 | semidirect |
| 168. C22×D4 | #10597010 | semidirect |
| 205. C2×D4 | C2×#10597010 | semidirect |
| 301. C2 | #23750623 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D149⋊M16 | 2 |
| C2×#18011990 | 2 |
| #23750623 | 2 |
| C2×#18011975 | 2 |
| C22×#14558735 | 2 |
| C2×#421 | 149 |