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×#15690843 | C2 | semidirect |
| 3. C2×#15690840 | C2 | semidirect |
| 4. C2×#15690810 | C2 | semidirect |
| 5. #20260919 | C2 | direct (N × H) |
| 6. C2×#15690738 | C2 | semidirect |
| 7. C2×#15690728 | C2 | semidirect |
| 8. C2×#104×C97 | C2 | semidirect |
| 22. #15690843 | C22 | semidirect |
| 24. #15690840 | C22 | semidirect |
| 31. #15690810 | C22 | semidirect |
| 33. #15690738 | C22 | semidirect |
| 34. #15690728 | C22 | semidirect |
| 38. #104×C97 | C22 | semidirect |
| 167. C2×C97 | #456 | semidirect |
| 171. C97 | C2×#456 | semidirect |
| 178. C2×#104 | D97 | semidirect |
| 208. #104 | C2×D97 | semidirect |
| 339. C2 | #20260919 | 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×#15690843 | 2 |
| C2×#15690840 | 2 |
| C2×#15690810 | 2 |
| #20260919 | 2 |
| C2×#15690738 | 2 |
| C2×#15690728 | 2 |
| C2×#104×C97 | 2 |
| C2×#456 | 97 |