Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23749934 | C2 | semidirect |
| 4. #23749923 | C2 | semidirect |
| 5. #23749913 | C2 | semidirect |
| 6. #23749908 | C2 | semidirect |
| 7. #23749667 | C2 | semidirect |
| 8. C2×#18011842 | C2 | semidirect |
| 9. #23749653 | C2 | semidirect |
| 64. #41×C149 | Q8 | semidirect |
| 123. C149 | #3084 | semidirect |
| 166. #41 | Dic298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750256 | 2 |
| #23750108 | 2 |
| #23749934 | 2 |
| #23749923 | 2 |
| #23749913 | 2 |
| #23749908 | 2 |
| #23749667 | 2 |
| C2×#18011842 | 2 |
| #23749653 | 2 |
| #23749621 | 2 |
| #417×C149 | 2 |
| #3084 | 149 |