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×#18012765 | C2 | semidirect |
| 3. #23752355 | C2 | semidirect |
| 4. #23752350 | C2 | semidirect |
| 5. #23752345 | C2 | semidirect |
| 6. #23752211 | C2 | semidirect |
| 7. #23752176 | C2 | semidirect |
| 8. C2×#121×C151 | C2 | semidirect |
| 13. C2×#14559004 | C22 | semidirect |
| 14. C22×Dic302 | C22 | semidirect |
| 15. C22×D604 | C22 | semidirect |
| 19. C2×#14558992 | C22 | semidirect |
| 20. C2×#14558989 | C22 | semidirect |
| 21. C2×#14558988 | C22 | semidirect |
| 22. #18012662 | C22 | semidirect |
| 23. #18012659 | C22 | semidirect |
| 24. C22⋊(C151⋊C8) | C22 | semidirect |
| 25. C22⋊(C151⋊C8) | C22 | semidirect |
| 27. C22×D4×C151 | C22 | semidirect |
| 32. #121×C151 | C22 | semidirect |
| 33. C2×C4⋊C4×C151 | C22 | semidirect |
| 41. #14559004 | D4 | semidirect |
| 85. Dic302 | C2×D4 | semidirect |
| 88. D604 | C2×D4 | semidirect |
| 135. C22×C151 | AGL(1,ℤ/8) | semidirect |
| 155. C151 | #3006 | semidirect |
| 159. C2×#121 | D151 | semidirect |
| 174. C22×D4 | C2×D151 | semidirect |
| 184. #121 | C2×D151 | semidirect |
| 185. C2×C4⋊C4 | C2×D151 | semidirect |
| 295. C22 | #18012765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14559004 | 2 |
| C2×#18012765 | 2 |
| #23752355 | 2 |
| #23752350 | 2 |
| #23752345 | 2 |
| #23752211 | 2 |
| #23752176 | 2 |
| C2×#121×C151 | 2 |
| #3006 | 151 |