Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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×#18011934 | C2 | semidirect |
| 2. #23750294 | C2 | semidirect |
| 3. #23750000 | C2 | semidirect |
| 4. #23749861 | C2 | semidirect |
| 5. #23749858 | C2 | semidirect |
| 6. #23749823 | C2 | semidirect |
| 7. #23749770 | C2 | semidirect |
| 8. #23749769 | C2 | semidirect |
| 9. Q16×Dic149 | C2 | semidirect |
| 10. C8×C22⋊D149 | C2 | semidirect |
| 11. C2×#135×C149 | C2 | semidirect |
| 74. Q16×C149 | D4 | semidirect |
| 134. Dic149 | #135 | semidirect |
| 142. C149 | #3287 | semidirect |
| 145. C2×#135 | D149 | semidirect |
| 202. Q16 | C22⋊D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011934 | 2 |
| #23750294 | 2 |
| #23750000 | 2 |
| #23749861 | 2 |
| #23749858 | 2 |
| #23749823 | 2 |
| #23749770 | 2 |
| #23749769 | 2 |
| Q16×Dic149 | 2 |
| C8×C22⋊D149 | 2 |
| C2×#135×C149 | 2 |
| #3287 | 149 |