Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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×#18012764 | C2 | semidirect |
| 2. C2×#18012764 | C2 | semidirect |
| 3. #23752979 | C2 | semidirect |
| 4. #23752480 | C2 | semidirect |
| 5. #23752477 | C2 | semidirect |
| 6. #23752260 | C2 | semidirect |
| 7. #23752196 | C2 | semidirect |
| 8. C2×#18012655 | C2 | semidirect |
| 9. #575×C151 | C2 | semidirect |
| 16. C2×#14558991 | C22 | semidirect |
| 18. C2×#14558989 | C22 | semidirect |
| 20. #18012746 | C22 | semidirect |
| 25. #18012674 | C22 | semidirect |
| 26. #18012658 | C22 | semidirect |
| 27. #18012656 | C22 | semidirect |
| 28. #18012655 | C22 | semidirect |
| 32. #137×C151 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C151 | C22 | semidirect |
| 147. C151 | #3068 | semidirect |
| 149. #575 | D151 | semidirect |
| 162. #137 | C2×D151 | semidirect |
| 168. AGL(1,ℤ/8) | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012764 | 2 |
| #23752979 | 2 |
| #23752480 | 2 |
| #23752477 | 2 |
| #23752260 | 2 |
| #23752196 | 2 |
| C2×#18012655 | 2 |
| #575×C151 | 2 |
| #3068 | 151 |