Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
414 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 2. #23749963 | C2 | semidirect |
| 3. #23749960 | C2 | semidirect |
| 4. #23749943 | C2 | semidirect |
| 5. #23749881 | C2 | semidirect |
| 6. #23749873 | C2 | semidirect |
| 7. #23749785 | C2 | semidirect |
| 8. #23749781 | C2 | semidirect |
| 9. #23749764 | C2 | semidirect |
| 10. #23749589 | C2 | semidirect |
| 11. C2×C22⋊Q8×C149 | C2 | semidirect |
| 13. C2×#14558726 | C22 | semidirect |
| 14. C2×#14558723 | C22 | semidirect |
| 25. #18011844 | C22 | semidirect |
| 26. #18011842 | C22 | semidirect |
| 27. #18011835 | C22 | semidirect |
| 28. #18011835 | C22 | semidirect |
| 29. #18011834 | C22 | semidirect |
| 30. #18011831 | C22 | semidirect |
| 149. C149 | #3196 | semidirect |
| 152. C2×C22⋊Q8 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750136 | 2 |
| #23749963 | 2 |
| #23749960 | 2 |
| #23749943 | 2 |
| #23749881 | 2 |
| #23749873 | 2 |
| #23749785 | 2 |
| #23749781 | 2 |
| #23749764 | 2 |
| #23749589 | 2 |
| C2×C22⋊Q8×C149 | 2 |
| #3196 | 149 |