Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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×#18011899 | C2 | semidirect |
| 2. #23750012 | C2 | semidirect |
| 3. #23749987 | C2 | semidirect |
| 4. #23749840 | C2 | semidirect |
| 5. #23749763 | C2 | semidirect |
| 6. #23749758 | C2 | semidirect |
| 7. #23749682 | C2 | semidirect |
| 8. #532×C149 | C2 | semidirect |
| 11. C2×#14558724 | C22 | semidirect |
| 19. C4⋊#11924746 | C22 | semidirect |
| 20. #18011834 | C22 | semidirect |
| 23. #18011822 | C22 | semidirect |
| 25. C4⋊Q8×C149 | C22 | semidirect |
| 26. #127×C149 | C22 | semidirect |
| 31. C4×D4×C149 | C22 | semidirect |
| 120. C149 | #3213 | semidirect |
| 122. #532 | D149 | semidirect |
| 135. C4⋊Q8 | C2×D149 | semidirect |
| 136. #127 | C2×D149 | semidirect |
| 145. C4×D4 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011899 | 2 |
| #23750012 | 2 |
| #23749987 | 2 |
| #23749840 | 2 |
| #23749763 | 2 |
| #23749758 | 2 |
| #23749682 | 2 |
| #532×C149 | 2 |
| #3213 | 149 |