Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23750256 | C2 | semidirect |
| 3. #23749931 | C2 | semidirect |
| 4. #23749928 | C2 | semidirect |
| 5. #23749919 | C2 | semidirect |
| 6. #23749904 | C2 | semidirect |
| 7. #23749665 | C2 | semidirect |
| 8. #23749651 | C2 | semidirect |
| 11. C2×#107×C149 | C2 | semidirect |
| 42. #14558736 | Q8 | semidirect |
| 123. C149 | #3083 | semidirect |
| 132. C2×#107 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750256 | 2 |
| #23750106 | 2 |
| #23749931 | 2 |
| #23749928 | 2 |
| #23749919 | 2 |
| #23749904 | 2 |
| #23749665 | 2 |
| #23749651 | 2 |
| #23749624 | 2 |
| #23749622 | 2 |
| C2×#107×C149 | 2 |
| #3083 | 149 |