Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
544 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 2. C2×C4×Dic302 | C2 | semidirect |
| 3. #23752312 | C2 | direct (N × H) |
| 4. C2×#18012672 | C2 | semidirect |
| 5. C2×#18012662 | C2 | semidirect |
| 7. C2×#18012650 | C2 | semidirect |
| 10. C2×#14558992 | C4 | semidirect |
| 15. C4×Dic302 | C22 | semidirect |
| 19. #18012672 | C22 | semidirect |
| 20. #18012662 | C22 | semidirect |
| 22. #18012650 | C22 | semidirect |
| 32. C2×Dic302 | C2×C4 | semidirect |
| 36. #14558992 | C2×C4 | semidirect |
| 38. C2×C151⋊C8 | C2×C4 | semidirect |
| 63. Dic302 | C22×C4 | semidirect |
| 69. C151⋊C8 | C22×C4 | semidirect |
| 106. C2×C151 | #440 | semidirect |
| 110. C151 | C2×#440 | semidirect |
| 217. C2 | #23752312 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558992 | 2 |
| C2×C4×Dic302 | 2 |
| #23752312 | 2 |
| C2×#18012672 | 2 |
| C2×#18012662 | 2 |
| C2×#18012660 | 2 |
| C2×#18012650 | 2 |
| C2×C4×D4×C151 | 2 |
| C2×#440 | 151 |