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 |
|---|---|---|
| 1. C22×#14558724 | C2 | semidirect |
| 2. #23750196 | C2 | semidirect |
| 3. #23750100 | C2 | semidirect |
| 4. #23749838 | C2 | semidirect |
| 5. #23749828 | C2 | semidirect |
| 6. #23749653 | C2 | semidirect |
| 7. #23749635 | C2 | semidirect |
| 8. #23749621 | C2 | semidirect |
| 14. #18011909 | C22 | semidirect |
| 15. #18011898 | C22 | semidirect |
| 23. #18011840 | C22 | semidirect |
| 24. #18011836 | C22 | semidirect |
| 25. #18011835 | C22 | semidirect |
| 26. #18011832 | C22 | semidirect |
| 116. C149 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558724 | 2 |
| #23750196 | 2 |
| #23750100 | 2 |
| #23749838 | 2 |
| #23749828 | 2 |
| #23749653 | 2 |
| #23749635 | 2 |
| #23749621 | 2 |
| C2×AGL(1,ℤ/8)×C149 | 2 |
| #3042 | 149 |