Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#14558726 | C2 | semidirect |
| 5. #23749882 | C2 | direct (N × H) |
| 6. C2×#18011842 | C2 | semidirect |
| 7. C2×#18011836 | C2 | semidirect |
| 8. C2×#103×C149 | C2 | semidirect |
| 12. C2×#14558726 | C22 | semidirect |
| 25. #18011842 | C22 | semidirect |
| 26. #18011836 | C22 | semidirect |
| 30. #103×C149 | C22 | semidirect |
| 110. C2×C149 | #470 | semidirect |
| 115. C149 | C2×#470 | semidirect |
| 124. C2×#103 | D149 | semidirect |
| 146. #103 | C2×D149 | semidirect |
| 227. C2 | #23749882 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558726 | 2 |
| C22×#14558719 | 2 |
| C2×#18011891 | 2 |
| C2×#18011887 | 2 |
| #23749882 | 2 |
| C2×#18011842 | 2 |
| C2×#18011836 | 2 |
| C2×#103×C149 | 2 |
| C2×#470 | 149 |