Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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. #23750332 | C2 | semidirect |
| 2. #23750021 | C2 | semidirect |
| 3. #23749955 | C2 | semidirect |
| 4. #23749941 | C2 | semidirect |
| 5. #23749915 | C2 | semidirect |
| 6. #23749907 | C2 | semidirect |
| 7. #23749852 | C2 | semidirect |
| 8. C4×#14558724 | C2 | semidirect |
| 9. D4×#11924746 | C2 | semidirect |
| 10. C2×#18011842 | C2 | semidirect |
| 83. #11924746 | #41 | semidirect |
| 90. D4×C149 | SD16 | semidirect |
| 123. C149 | #3335 | semidirect |
| 207. D4 | #14558724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750332 | 2 |
| #23750021 | 2 |
| #23749955 | 2 |
| #23749941 | 2 |
| #23749915 | 2 |
| #23749907 | 2 |
| #23749852 | 2 |
| C4×#14558724 | 2 |
| D4×#11924746 | 2 |
| C2×#18011842 | 2 |
| #547×C149 | 2 |
| #3335 | 149 |