Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
468 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 137 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×#18011890 | C2 | semidirect |
| 3. #23749956 | C2 | semidirect |
| 4. #23749944 | C2 | semidirect |
| 5. #23749854 | C2 | semidirect |
| 6. #23749778 | C2 | semidirect |
| 7. #23749766 | C2 | semidirect |
| 8. C2×C22⋊C8×C149 | C2 | semidirect |
| 9. C22×Dic298 | C22 | semidirect |
| 12. C2×#14558725 | C22 | semidirect |
| 16. #18011890 | C22 | semidirect |
| 22. C2×C4⋊Dic149 | C22 | semidirect |
| 26. #18011843 | C22 | semidirect |
| 27. #18011836 | C22 | semidirect |
| 28. #18011833 | C22 | semidirect |
| 30. C22×C8×C149 | C22 | semidirect |
| 32. C22⋊C8×C149 | C22 | semidirect |
| 85. C23×C149 | SD16 | semidirect |
| 129. C149 | #3187 | semidirect |
| 138. C2×C22⋊C8 | D149 | semidirect |
| 144. C22×C8 | C2×D149 | semidirect |
| 162. C22⋊C8 | C2×D149 | semidirect |
| 203. C23 | #14558725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011890 | 2 |
| C2×#18011885 | 2 |
| #23749956 | 2 |
| #23749944 | 2 |
| #23749854 | 2 |
| #23749778 | 2 |
| #23749766 | 2 |
| C2×C22⋊C8×C149 | 2 |
| #3187 | 149 |