Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
368 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 69 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×#15690725 | C2 | semidirect |
| 3. #20260527 | C2 | direct (N × H) |
| 4. C2×#99×C97 | C2 | semidirect |
| 5. C22×D388 | C4 | semidirect |
| 10. #15690806 | C4 | semidirect |
| 13. C2×C4×Dic97 | C4 | semidirect |
| 15. #15690725 | C22 | semidirect |
| 19. #99×C97 | C22 | semidirect |
| 24. C2×D388 | C2×C4 | semidirect |
| 36. C4×Dic97 | C2×C4 | semidirect |
| 117. C2×C97 | #353 | semidirect |
| 121. C97 | C2×#353 | semidirect |
| 124. C2×#99 | D97 | semidirect |
| 140. #99 | C2×D97 | semidirect |
| 239. C2 | #20260527 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690806 | 2 |
| C2×#15690725 | 2 |
| #20260527 | 2 |
| C2×#99×C97 | 2 |
| C2×#353 | 97 |