Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1880 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 645 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×#15690799 | C2 | direct (N × H) |
| 3. C22×#13095488 | C2 | semidirect |
| 4. C22×C4×Dic97 | C2 | semidirect |
| 5. C23×Q8×C97 | C2 | semidirect |
| 10. #15690799 | C22 | direct (N × H) |
| 11. C2×#13095488 | C22 | semidirect |
| 12. C2×C4×Dic97 | C22 | semidirect |
| 14. C22×Q8×C97 | C22 | semidirect |
| 24. #13095488 | C23 | semidirect |
| 25. C4×Dic97 | C23 | semidirect |
| 28. C2×Q8×C97 | C23 | semidirect |
| 48. C22×C97 | #124 | semidirect |
| 58. C2×C97 | C2×#124 | semidirect |
| 63. C97 | C22×#124 | semidirect |
| 64. C23×Q8 | D97 | semidirect |
| 71. C22×Q8 | C2×D97 | semidirect |
| 85. C2×Q8 | C22×D97 | semidirect |
| 114. C22 | #15690799 | direct (N × H) |
| 122. C2 | C2×#15690799 | 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×#15690799 | 2 |
| C22×#13095488 | 2 |
| C22×C4×Dic97 | 2 |
| C23×Q8×C97 | 2 |
| C22×#124 | 97 |