Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 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. C2×#18011944 | C2 | semidirect |
| 2. C22×#14558725 | C2 | semidirect |
| 4. #23750102 | C2 | semidirect |
| 5. #23749848 | C2 | semidirect |
| 6. #23749826 | C2 | semidirect |
| 7. #23749631 | C2 | semidirect |
| 8. #23749622 | C2 | semidirect |
| 9. #424×C149 | C2 | semidirect |
| 14. C2×Dic596 | C22 | semidirect |
| 17. C2×#14558725 | C22 | semidirect |
| 22. C4×Dic298 | C22 | semidirect |
| 26. #18011836 | C22 | semidirect |
| 28. #18011833 | C22 | semidirect |
| 32. C4⋊C8×C149 | C22 | semidirect |
| 38. C2×Dic298 | D4 | semidirect |
| 116. C149 | #3043 | semidirect |
| 124. #424 | D149 | semidirect |
| 146. C4⋊C8 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011944 | 2 |
| C22×#14558725 | 2 |
| #23750194 | 2 |
| #23750102 | 2 |
| #23749848 | 2 |
| #23749826 | 2 |
| #23749631 | 2 |
| #23749622 | 2 |
| #424×C149 | 2 |
| #3043 | 149 |