Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
360 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 109 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. C42×Dic149 | C2 | semidirect |
| 6. #23749384 | C2 | semidirect |
| 7. #339×C149 | C2 | semidirect |
| 10. #18011876 | C4 | semidirect |
| 11. #18011873 | C4 | semidirect |
| 18. #18011839 | C4 | semidirect |
| 19. #18011837 | C4 | semidirect |
| 37. #14558720 | C2×C4 | semidirect |
| 45. C4×Dic149 | C2×C4 | semidirect |
| 51. M16×C149 | C2×C4 | semidirect |
| 57. C42×C149 | C2×C4 | semidirect |
| 60. Dic298 | C42 | semidirect |
| 62. D596 | C42 | semidirect |
| 101. Dic149 | #104 | semidirect |
| 107. C149 | C4×#104 | semidirect |
| 115. #339 | D149 | semidirect |
| 149. M16 | C4×D149 | semidirect |
| 165. 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 |
| C42×Dic149 | 2 |
| #23749384 | 2 |
| #339×C149 | 2 |
| C4×#104 | 149 |