Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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. C2×#18012769 | C2 | semidirect |
| 2. C2×#18012726 | C2 | semidirect |
| 3. #41×Dic151 | C2 | semidirect |
| 4. #23752432 | C2 | semidirect |
| 5. #23752425 | C2 | semidirect |
| 6. #23752235 | C2 | semidirect |
| 7. #23752222 | C2 | semidirect |
| 8. #23752217 | C2 | semidirect |
| 12. C2×#14558994 | C22 | semidirect |
| 13. C2×#14558992 | C22 | semidirect |
| 18. Q8×Dic151 | C22 | semidirect |
| 20. D4×Dic151 | C22 | semidirect |
| 26. Dic151⋊C8 | C22 | semidirect |
| 27. #18012664 | C22 | semidirect |
| 125. C151 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012769 | 2 |
| C2×#18012726 | 2 |
| #41×Dic151 | 2 |
| #23752432 | 2 |
| #23752425 | 2 |
| #23752235 | 2 |
| #23752222 | 2 |
| #23752217 | 2 |
| C2×AGL(1,ℤ/8)×C151 | 2 |
| #3040 | 151 |