Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 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 |
|---|---|---|
| 2. C2×#18012770 | C2 | semidirect |
| 3. #23752786 | C2 | semidirect |
| 4. #23752393 | C2 | semidirect |
| 5. #23752388 | C2 | semidirect |
| 6. #23752229 | C2 | semidirect |
| 7. #23752228 | C2 | semidirect |
| 8. #23752194 | C2 | semidirect |
| 9. C2×#137×C151 | C2 | semidirect |
| 23. #18012770 | C22 | semidirect |
| 26. C2×#14558988 | C22 | semidirect |
| 27. #18012737 | C22 | semidirect |
| 28. #18012728 | C22 | semidirect |
| 31. #18012698 | C22 | semidirect |
| 32. #18012666 | C22 | semidirect |
| 33. #18012665 | C22 | semidirect |
| 34. #18012657 | C22 | semidirect |
| 35. #18012655 | C22 | semidirect |
| 37. C22×Q8×C151 | C22 | semidirect |
| 39. #137×C151 | C22 | semidirect |
| 42. C2×M16×C151 | C22 | semidirect |
| 192. C151 | #3022 | semidirect |
| 196. C2×#137 | D151 | semidirect |
| 216. C22×Q8 | C2×D151 | semidirect |
| 220. #137 | C2×D151 | semidirect |
| 226. C2×M16 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23753048 | 2 |
| C2×#18012770 | 2 |
| #23752786 | 2 |
| #23752393 | 2 |
| #23752388 | 2 |
| #23752229 | 2 |
| #23752228 | 2 |
| #23752194 | 2 |
| C2×#137×C151 | 2 |
| #3022 | 151 |