Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1880 conjugacy classes of subgroups; only the 661 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 661 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×#15690717 | C2 | semidirect |
| 3. #95×D97 | C2 | direct (N × H) |
| 4. C2×#95×C97 | C2 | semidirect |
| 8. C22×C4×D97 | C4 | semidirect |
| 10. #15690717 | C22 | semidirect |
| 12. #95×C97 | C22 | semidirect |
| 18. C22×Dic97 | C2×C4 | semidirect |
| 22. C2×C4×D97 | C2×C4 | semidirect |
| 25. C22×C4×C97 | C2×C4 | semidirect |
| 39. C2×C4×C97 | C22×C4 | semidirect |
| 42. C2×Dic97 | C22×C4 | semidirect |
| 50. C2×D97 | #95 | direct (N × H) |
| 56. C2×C97 | C2×#95 | semidirect |
| 60. D97 | C2×#95 | direct (N × H) |
| 62. C97 | C22×#95 | semidirect |
| 66. C2×#95 | D97 | direct (N × H) |
| 74. #95 | C2×D97 | direct (N × H) |
| 87. C22×C4 | C4×D97 | semidirect |
| 105. C2×C4 | C2×C4×D97 | semidirect |
| 119. C2 | #95×D97 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D97 | 2 |
| C2×#15690717 | 2 |
| #95×D97 | 2 |
| C2×#95×C97 | 2 |
| C22×#95 | 97 |