Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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. C22×#14559004 | C2 | semidirect |
| 2. C2×#18012767 | C2 | semidirect |
| 3. C2×#18012713 | C2 | semidirect |
| 4. #23752359 | C2 | semidirect |
| 5. #23752353 | C2 | semidirect |
| 6. #23752348 | C2 | semidirect |
| 7. #23752214 | C2 | semidirect |
| 8. #407×C151 | C2 | semidirect |
| 13. C2×#14559004 | C22 | semidirect |
| 14. C22×Dic302 | C22 | semidirect |
| 15. C22×D604 | C22 | semidirect |
| 16. C22×D604 | C22 | semidirect |
| 21. C2×#14558993 | C22 | semidirect |
| 22. C2×D1208 | C22 | semidirect |
| 26. #18012713 | C22 | semidirect |
| 27. C2×C4⋊Dic151 | C22 | semidirect |
| 29. #18012664 | C22 | semidirect |
| 30. #18012661 | C22 | semidirect |
| 32. C2×M16×C151 | C22 | semidirect |
| 33. C22⋊C8×C151 | C22 | semidirect |
| 34. C22⋊C8×C151 | C22 | semidirect |
| 42. #14559004 | D4 | semidirect |
| 89. Dic302 | C2×D4 | semidirect |
| 94. D604 | C2×D4 | semidirect |
| 131. C22×C151 | AGL(1,ℤ/8) | semidirect |
| 155. C151 | #3006 | semidirect |
| 164. #407 | D151 | semidirect |
| 180. C2×M16 | C2×D151 | semidirect |
| 189. C22⋊C8 | C2×D151 | semidirect |
| 190. C22⋊C8 | C2×D151 | semidirect |
| 295. C22 | #18012767 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14559004 | 2 |
| C2×#18012767 | 2 |
| C2×#18012713 | 2 |
| #23752359 | 2 |
| #23752353 | 2 |
| #23752348 | 2 |
| #23752214 | 2 |
| #407×C151 | 2 |
| #3006 | 151 |