Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 2. C22×#14558723 | C2 | semidirect |
| 3. #23750099 | C2 | semidirect |
| 4. #23749837 | C2 | semidirect |
| 5. #23749827 | C2 | semidirect |
| 6. #23749652 | C2 | semidirect |
| 7. #23749634 | C2 | semidirect |
| 8. #23749621 | C2 | semidirect |
| 9. #536×C149 | C2 | semidirect |
| 22. C4⋊#11924746 | C22 | semidirect |
| 23. #18011835 | C22 | semidirect |
| 24. #18011835 | C22 | semidirect |
| 25. #18011832 | C22 | semidirect |
| 28. C4⋊Q8×C149 | C22 | semidirect |
| 29. #124×C149 | C22 | semidirect |
| 116. C149 | #3042 | semidirect |
| 120. #536 | D149 | semidirect |
| 137. C4⋊Q8 | C2×D149 | semidirect |
| 138. #124 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011936 | 2 |
| C22×#14558723 | 2 |
| #23750099 | 2 |
| #23749837 | 2 |
| #23749827 | 2 |
| #23749652 | 2 |
| #23749634 | 2 |
| #23749621 | 2 |
| #536×C149 | 2 |
| #3042 | 149 |