Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15690857 | C2 | semidirect |
| 2. C2×#15690836 | C2 | semidirect |
| 3. C2×#15690797 | C2 | semidirect |
| 4. #20260906 | C2 | direct (N × H) |
| 5. C2×#15690737 | C2 | semidirect |
| 6. C2×#15690736 | C2 | semidirect |
| 7. C2×#15690728 | C2 | semidirect |
| 8. C2×AGL(1,ℤ/8)×C97 | C2 | semidirect |
| 12. #15690857 | C22 | semidirect |
| 21. #15690836 | C22 | semidirect |
| 26. #15690797 | C22 | semidirect |
| 29. #15690737 | C22 | semidirect |
| 30. #15690736 | C22 | semidirect |
| 31. #15690728 | C22 | semidirect |
| 35. AGL(1,ℤ/8)×C97 | C22 | semidirect |
| 172. C2×C97 | #454 | semidirect |
| 176. C97 | C2×#454 | semidirect |
| 179. C2×AGL(1,ℤ/8) | D97 | semidirect |
| 201. AGL(1,ℤ/8) | C2×D97 | semidirect |
| 349. C2 | #20260906 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690857 | 2 |
| C2×#15690836 | 2 |
| C2×#15690797 | 2 |
| #20260906 | 2 |
| C2×#15690737 | 2 |
| C2×#15690736 | 2 |
| C2×#15690728 | 2 |
| C2×AGL(1,ℤ/8)×C97 | 2 |
| C2×#454 | 97 |