Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23750162 | C2 | semidirect |
| 2. #23750026 | C2 | semidirect |
| 3. #23750010 | C2 | semidirect |
| 4. #23749981 | C2 | semidirect |
| 5. #23749863 | C2 | semidirect |
| 7. #23749857 | C2 | semidirect |
| 8. C4×#14558723 | C2 | semidirect |
| 9. C4×D1192 | C2 | semidirect |
| 10. C4×C8×D149 | C2 | semidirect |
| 11. C4×Q16×C149 | C2 | semidirect |
| 118. C149 | #3168 | semidirect |
| 127. C4×Q16 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750162 | 2 |
| #23750026 | 2 |
| #23750010 | 2 |
| #23749981 | 2 |
| #23749863 | 2 |
| #23749862 | 2 |
| #23749857 | 2 |
| C4×#14558723 | 2 |
| C4×D1192 | 2 |
| C4×C8×D149 | 2 |
| C4×Q16×C149 | 2 |
| #3168 | 149 |