Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14558994 | C2 | semidirect |
| 4. C2×#18012737 | C2 | semidirect |
| 6. #23752605 | C2 | direct (N × H) |
| 7. C2×#18012649 | C2 | semidirect |
| 8. C22×Q16×C151 | C2 | semidirect |
| 12. C2×#14558994 | C22 | semidirect |
| 19. #18012737 | C22 | semidirect |
| 25. #18012649 | C22 | semidirect |
| 29. C2×Q16×C151 | C22 | semidirect |
| 108. C2×C151 | #497 | semidirect |
| 112. C151 | C2×#497 | semidirect |
| 115. C22×Q16 | D151 | semidirect |
| 129. C2×Q16 | C2×D151 | semidirect |
| 222. C2 | #23752605 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558994 | 2 |
| C22×#14558993 | 2 |
| C22×#14558991 | 2 |
| C2×#18012737 | 2 |
| C2×#18012728 | 2 |
| #23752605 | 2 |
| C2×#18012649 | 2 |
| C22×Q16×C151 | 2 |
| C2×#497 | 151 |