Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
536 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 3. #23752255 | C2 | direct (N × H) |
| 4. C2×#18012672 | C2 | semidirect |
| 5. C2×#18012670 | C2 | semidirect |
| 8. C2×#14558988 | C4 | semidirect |
| 15. #18012672 | C22 | semidirect |
| 16. #18012670 | C22 | semidirect |
| 27. #14558988 | C2×C4 | semidirect |
| 28. C2×C151⋊C8 | C2×C4 | semidirect |
| 51. C151⋊C8 | C22×C4 | semidirect |
| 86. C2×C151 | #428 | semidirect |
| 90. C151 | C2×#428 | semidirect |
| 177. C2 | #23752255 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558988 | 2 |
| C22×C4⋊Dic151 | 2 |
| #23752255 | 2 |
| C2×#18012672 | 2 |
| C2×#18012670 | 2 |
| C2×#117×C151 | 2 |
| C2×#428 | 151 |