Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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×#18011910 | C2 | semidirect |
| 3. #23749986 | C2 | semidirect |
| 4. #23749983 | C2 | semidirect |
| 5. #23749974 | C2 | semidirect |
| 6. #23749970 | C2 | semidirect |
| 7. #23749627 | C2 | semidirect |
| 8. #23749626 | C2 | semidirect |
| 9. #23749624 | C2 | semidirect |
| 10. M16×Dic149 | C2 | semidirect |
| 11. #417×C149 | C2 | semidirect |
| 149. C149 | #3141 | semidirect |
| 160. #417 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750171 | 2 |
| C2×#18011910 | 2 |
| #23749986 | 2 |
| #23749983 | 2 |
| #23749974 | 2 |
| #23749970 | 2 |
| #23749627 | 2 |
| #23749626 | 2 |
| #23749624 | 2 |
| M16×Dic149 | 2 |
| #417×C149 | 2 |
| #3141 | 149 |