Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 708 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 |
|---|---|---|
| 2. C2×#15690841 | C2 | semidirect |
| 3. C2×#15690808 | C2 | semidirect |
| 4. #20260916 | C2 | direct (N × H) |
| 5. C2×#15690737 | C2 | semidirect |
| 6. C2×#15690736 | C2 | semidirect |
| 7. C2×#15690728 | C2 | semidirect |
| 8. C2×#137×C97 | C2 | semidirect |
| 21. #15690841 | C22 | semidirect |
| 26. #15690808 | C22 | semidirect |
| 29. #15690737 | C22 | semidirect |
| 30. #15690736 | C22 | semidirect |
| 31. #15690728 | C22 | semidirect |
| 35. #137×C97 | C22 | semidirect |
| 167. C2×C97 | #456 | semidirect |
| 171. C97 | C2×#456 | semidirect |
| 174. C2×#137 | D97 | semidirect |
| 196. #137 | C2×D97 | semidirect |
| 339. C2 | #20260916 | 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×#15690841 | 2 |
| C2×#15690808 | 2 |
| #20260916 | 2 |
| C2×#15690737 | 2 |
| C2×#15690736 | 2 |
| C2×#15690728 | 2 |
| C2×#137×C97 | 2 |
| C2×#456 | 97 |