Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18012784 | C2 | semidirect |
| 2. C2×#18012765 | C2 | semidirect |
| 3. #23752779 | C2 | semidirect |
| 4. #23752354 | C2 | semidirect |
| 5. #23752344 | C2 | semidirect |
| 6. #23752217 | C2 | semidirect |
| 7. #23752209 | C2 | semidirect |
| 8. #23752178 | C2 | semidirect |
| 9. C22×D8×C151 | C2 | semidirect |
| 15. C2×#14559003 | C22 | semidirect |
| 18. C2×D4×D151 | C22 | semidirect |
| 20. C2×#14558992 | C22 | semidirect |
| 21. C2×#14558989 | C22 | semidirect |
| 22. C2×#14558988 | C22 | semidirect |
| 25. #18012710 | C22 | semidirect |
| 27. #18012698 | C22 | semidirect |
| 28. #18012664 | C22 | semidirect |
| 29. #18012661 | C22 | semidirect |
| 30. #18012660 | C22 | semidirect |
| 31. (C2×D151)⋊C8 | C22 | semidirect |
| 33. C22×D4×C151 | C22 | semidirect |
| 35. C2×D8×C151 | C22 | semidirect |
| 36. C22×C8×C151 | C22 | semidirect |
| 41. #14559004 | D4 | semidirect |
| 76. C2×D4×C151 | D4 | semidirect |
| 151. C151 | #3008 | semidirect |
| 155. C22×D8 | D151 | semidirect |
| 172. C22×D4 | C2×D151 | semidirect |
| 177. C2×D8 | C2×D151 | semidirect |
| 179. C22×C8 | C2×D151 | semidirect |
| 217. C2×D4 | C22⋊D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012784 | 2 |
| C2×#18012765 | 2 |
| #23752779 | 2 |
| #23752354 | 2 |
| #23752344 | 2 |
| #23752217 | 2 |
| #23752209 | 2 |
| #23752178 | 2 |
| C22×D8×C151 | 2 |
| #3008 | 151 |