Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
404 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 404 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. #23750354 | C2 | semidirect |
| 2. #23749997 | C2 | semidirect |
| 3. #23749830 | C2 | semidirect |
| 4. #23749822 | C2 | semidirect |
| 5. Q8×#11924746 | C2 | semidirect |
| 6. C4×#14558724 | C2 | semidirect |
| 49. #11924746 | #41 | semidirect |
| 51. Q8×C149 | SD16 | semidirect |
| 76. C149 | #3392 | semidirect |
| 124. Q8 | #14558724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750354 | 2 |
| #23749997 | 2 |
| #23749830 | 2 |
| #23749822 | 2 |
| Q8×#11924746 | 2 |
| C4×#14558724 | 2 |
| #550×C149 | 2 |
| #3392 | 149 |