Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
168 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 51 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. #23749907 | C2 | semidirect |
| 4. #23749752 | C2 | semidirect |
| 5. #23749377 | C2 | semidirect |
| 7. #332×C149 | C2 | semidirect |
| 54. #11924746 | SD16 | semidirect |
| 79. C149 | #1686 | semidirect |
| 86. #332 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23749999 | 2 |
| #23749907 | 2 |
| #23749826 | 2 |
| #23749752 | 2 |
| #23749377 | 2 |
| #23749368 | 2 |
| #332×C149 | 2 |
| #1686 | 149 |