Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
336 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. C2×#18011839 | C2 | semidirect |
| 3. C2×#18011838 | C2 | semidirect |
| 4. C2×#18011837 | C2 | semidirect |
| 5. M16×Dic149 | C2 | semidirect |
| 6. C4×#14558715 | C2 | semidirect |
| 7. C2×#104×C149 | C2 | semidirect |
| 10. #18011909 | C4 | semidirect |
| 11. #18011907 | C4 | semidirect |
| 12. #18011900 | C4 | semidirect |
| 13. #18011898 | C4 | semidirect |
| 45. #14558720 | D4 | semidirect |
| 71. M16×C149 | D4 | semidirect |
| 140. Dic149 | #104 | semidirect |
| 148. C149 | #1980 | semidirect |
| 154. C2×#104 | D149 | semidirect |
| 206. M16 | C22⋊D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750171 | 2 |
| C2×#18011839 | 2 |
| C2×#18011838 | 2 |
| C2×#18011837 | 2 |
| M16×Dic149 | 2 |
| C4×#14558715 | 2 |
| C2×#104×C149 | 2 |
| #1980 | 149 |