Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
320 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. M16×Dic149 | C2 | semidirect |
| 5. #23749471 | C2 | semidirect |
| 6. #23749384 | C2 | semidirect |
| 7. #339×C149 | C2 | semidirect |
| 10. #18011876 | C4 | semidirect |
| 11. #18011873 | C4 | semidirect |
| 17. #18011839 | C4 | semidirect |
| 18. #18011837 | C4 | semidirect |
| 37. #14558720 | C2×C4 | semidirect |
| 44. C4×Dic149 | C2×C4 | semidirect |
| 50. M16×C149 | C2×C4 | semidirect |
| 56. C42×C149 | C2×C4 | semidirect |
| 106. C149 | #1759 | semidirect |
| 114. #339 | D149 | semidirect |
| 148. M16 | C4×D149 | semidirect |
| 163. C42 | C4×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750093 | 2 |
| C2×#18011839 | 2 |
| C2×#18011837 | 2 |
| M16×Dic149 | 2 |
| #23749471 | 2 |
| #23749384 | 2 |
| #339×C149 | 2 |
| #1759 | 149 |