Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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×#18011936 | C2 | semidirect |
| 2. C2×C4×D596 | C2 | semidirect |
| 3. #23749837 | C2 | semidirect |
| 4. #23749827 | C2 | semidirect |
| 5. #23749817 | C2 | semidirect |
| 6. #23749649 | C2 | semidirect |
| 7. #23749626 | C2 | semidirect |
| 8. #532×C149 | C2 | semidirect |
| 21. C4⋊#11924746 | C22 | semidirect |
| 22. C4⋊#11924746 | C22 | semidirect |
| 23. #18011835 | C22 | semidirect |
| 24. #18011832 | C22 | semidirect |
| 26. C4⋊Q8×C149 | C22 | semidirect |
| 27. #127×C149 | C22 | semidirect |
| 28. #124×C149 | C22 | semidirect |
| 37. C2×D596 | D4 | semidirect |
| 119. C4×C149 | AGL(1,ℤ/8) | semidirect |
| 129. C149 | #3036 | semidirect |
| 132. #532 | D149 | semidirect |
| 146. C4⋊Q8 | C2×D149 | semidirect |
| 147. #127 | C2×D149 | semidirect |
| 148. #124 | C2×D149 | semidirect |
| 250. C4 | #18011936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011936 | 2 |
| C2×C4×D596 | 2 |
| #23749837 | 2 |
| #23749827 | 2 |
| #23749817 | 2 |
| #23749649 | 2 |
| #23749626 | 2 |
| #532×C149 | 2 |
| #3036 | 149 |