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×#18012772 | C2 | semidirect |
| 3. C2×#18012769 | C2 | semidirect |
| 4. #23752788 | C2 | semidirect |
| 5. #23752396 | C2 | semidirect |
| 6. #23752391 | C2 | semidirect |
| 7. #23752230 | C2 | semidirect |
| 8. #23752194 | C2 | semidirect |
| 9. #421×C151 | C2 | semidirect |
| 22. C22×Dic302 | C22 | semidirect |
| 24. #18012772 | C22 | semidirect |
| 26. #18012769 | C22 | semidirect |
| 31. C2×#14558988 | C22 | semidirect |
| 32. #18012739 | C22 | semidirect |
| 33. #18012727 | C22 | semidirect |
| 36. #18012667 | C22 | semidirect |
| 37. #18012657 | C22 | semidirect |
| 38. #18012655 | C22 | semidirect |
| 40. C2×M16×C151 | C22 | semidirect |
| 41. #117×C151 | C22 | semidirect |
| 42. #104×C151 | C22 | semidirect |
| 192. C151 | #3022 | semidirect |
| 201. #421 | D151 | semidirect |
| 226. C2×M16 | C2×D151 | semidirect |
| 231. #117 | C2×D151 | semidirect |
| 233. #104 | 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×#18012772 | 2 |
| C2×#18012769 | 2 |
| #23752788 | 2 |
| #23752396 | 2 |
| #23752391 | 2 |
| #23752230 | 2 |
| #23752194 | 2 |
| #421×C151 | 2 |
| #3022 | 151 |