Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1492 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 1063 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 |
|---|---|---|
| 1. #20261218 | C2 | semidirect |
| 2. #20261213 | C2 | semidirect |
| 3. #41×Dic97 | C2 | semidirect |
| 4. C2×Q8×Dic97 | C2 | semidirect |
| 14. 2−1+4×C97 | C4 | semidirect |
| 24. #41×C97 | C2×C4 | semidirect |
| 25. C2×Q8×C97 | C2×C4 | semidirect |
| 46. Dic97 | 2−1+4 | direct (N × H) |
| 52. C97 | C4×2−1+4 | semidirect |
| 58. 2−1+4 | Dic97 | direct (N × H) |
| 69. #41 | C2×Dic97 | semidirect |
| 70. C2×Q8 | C2×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261218 | 2 |
| #20261213 | 2 |
| #41×Dic97 | 2 |
| C2×Q8×Dic97 | 2 |
| C2×2−1+4×C97 | 2 |
| C4×2−1+4 | 97 |