Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15690840 | C2 | semidirect |
| 2. C22×#13095499 | C2 | semidirect |
| 3. C2×#15690817 | C2 | semidirect |
| 4. #20260996 | C2 | direct (N × H) |
| 5. C2×#15690745 | C2 | semidirect |
| 6. C2×#15690728 | C2 | semidirect |
| 7. C2×#15690727 | C2 | semidirect |
| 11. #15690840 | C22 | semidirect |
| 17. C2×#13095499 | C22 | semidirect |
| 19. #15690817 | C22 | semidirect |
| 25. #15690745 | C22 | semidirect |
| 26. #15690728 | C22 | semidirect |
| 27. #15690727 | C22 | semidirect |
| 136. C2×C97 | #471 | semidirect |
| 139. C97 | C2×#471 | semidirect |
| 275. C2 | #20260996 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690840 | 2 |
| C22×#13095499 | 2 |
| C2×#15690817 | 2 |
| #20260996 | 2 |
| C2×#15690745 | 2 |
| C2×#15690728 | 2 |
| C2×#15690727 | 2 |
| C2×AGL(1,ℤ/8)×C97 | 2 |
| C2×#471 | 97 |