Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#18012786 | C2 | semidirect |
| 2. #23753010 | C2 | semidirect |
| 3. #23752783 | C2 | semidirect |
| 4. #23752393 | C2 | semidirect |
| 5. #23752383 | C2 | semidirect |
| 6. #23752229 | C2 | semidirect |
| 7. #23752228 | C2 | semidirect |
| 8. C2×#18012657 | C2 | semidirect |
| 9. #575×C151 | C2 | semidirect |
| 21. #18012770 | C22 | semidirect |
| 23. #18012765 | C22 | semidirect |
| 27. #18012737 | C22 | semidirect |
| 28. #18012726 | C22 | semidirect |
| 32. #18012666 | C22 | semidirect |
| 33. #18012665 | C22 | semidirect |
| 34. #18012657 | C22 | semidirect |
| 38. #137×C151 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C151 | C22 | semidirect |
| 185. C151 | #3020 | semidirect |
| 189. #575 | D151 | semidirect |
| 212. #137 | C2×D151 | semidirect |
| 216. 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×#18012786 | 2 |
| #23753010 | 2 |
| #23752783 | 2 |
| #23752393 | 2 |
| #23752383 | 2 |
| #23752229 | 2 |
| #23752228 | 2 |
| C2×#18012657 | 2 |
| #575×C151 | 2 |
| #3020 | 151 |