Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23750348 | C2 | semidirect |
| 2. #23749987 | C2 | semidirect |
| 3. #23749977 | C2 | semidirect |
| 4. #23749917 | C2 | semidirect |
| 5. #23749902 | C2 | semidirect |
| 7. #23749830 | C2 | semidirect |
| 8. #23749756 | C2 | semidirect |
| 9. #23749725 | C2 | semidirect |
| 11. D4×Q8×C149 | C2 | semidirect |
| 122. C149 | #3367 | semidirect |
| 125. D4×Q8 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750348 | 2 |
| #23749987 | 2 |
| #23749977 | 2 |
| #23749917 | 2 |
| #23749902 | 2 |
| #23749840 | 2 |
| #23749830 | 2 |
| #23749756 | 2 |
| #23749725 | 2 |
| C4×#14558721 | 2 |
| D4×Q8×C149 | 2 |
| #3367 | 149 |