Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D151 | C2 | semidirect |
| 3. C2×#18012667 | C2 | semidirect |
| 4. C2×#18012665 | C2 | semidirect |
| 5. C4×(C2×D151)⋊C4 | C2 | semidirect |
| 6. #23751971 | C2 | semidirect |
| 7. #339×C151 | C2 | semidirect |
| 16. #18012719 | C4 | semidirect |
| 17. #18012719 | C4 | semidirect |
| 18. #18012714 | C4 | semidirect |
| 19. #18012714 | C4 | semidirect |
| 53. #14558988 | D4 | semidirect |
| 69. M16×C151 | D4 | semidirect |
| 139. C2×D151 | #104 | semidirect |
| 159. C151 | #1871 | semidirect |
| 167. #339 | D151 | semidirect |
| 218. M16 | D604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D151 | 2 |
| #23752724 | 2 |
| C2×#18012667 | 2 |
| C2×#18012665 | 2 |
| C4×(C2×D151)⋊C4 | 2 |
| #23751971 | 2 |
| #339×C151 | 2 |
| #1871 | 151 |