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. #23750253 | C2 | semidirect |
| 3. #23749935 | C2 | semidirect |
| 4. #23749924 | C2 | semidirect |
| 5. #23749919 | C2 | semidirect |
| 6. #23749904 | C2 | semidirect |
| 7. C2×#18011844 | C2 | semidirect |
| 8. #23749653 | C2 | semidirect |
| 11. #428×C149 | C2 | semidirect |
| 42. #14558736 | Q8 | semidirect |
| 123. C149 | #3083 | semidirect |
| 131. #428 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750253 | 2 |
| #23750106 | 2 |
| #23749935 | 2 |
| #23749924 | 2 |
| #23749919 | 2 |
| #23749904 | 2 |
| C2×#18011844 | 2 |
| #23749653 | 2 |
| #23749627 | 2 |
| #23749619 | 2 |
| #428×C149 | 2 |
| #3083 | 149 |