Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1008 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 269 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×#15690769 | C2 | semidirect |
| 3. #20260741 | C2 | direct (N × H) |
| 4. C2×#15690732 | C2 | semidirect |
| 5. C22×M16×C97 | C2 | semidirect |
| 10. C22×D388 | C4 | semidirect |
| 14. #15690769 | C22 | semidirect |
| 15. C2×C4⋊Dic97 | C22 | semidirect |
| 18. #15690732 | C22 | semidirect |
| 21. C2×M16×C97 | C22 | semidirect |
| 22. C22×C8×C97 | C22 | semidirect |
| 34. C2×D388 | C2×C4 | semidirect |
| 38. C4⋊Dic97 | C23 | semidirect |
| 50. C2×C8×C97 | C23 | semidirect |
| 93. C2×C97 | #418 | semidirect |
| 98. C97 | C2×#418 | semidirect |
| 100. C22×M16 | D97 | semidirect |
| 113. C2×M16 | C2×D97 | semidirect |
| 114. C22×C8 | C2×D97 | semidirect |
| 144. C2×C8 | C22×D97 | semidirect |
| 192. C2 | #20260741 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D388 | 2 |
| C2×#15690769 | 2 |
| #20260741 | 2 |
| C2×#15690732 | 2 |
| C22×M16×C97 | 2 |
| C2×#418 | 97 |