Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
196 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 59 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. D4×#11715906 | C2 | semidirect |
| 2. #20261825 | C2 | semidirect |
| 3. D4⋊#11715906 | C2 | semidirect |
| 4. C8×#11715906 | C2 | semidirect |
| 27. D776 | C8 | semidirect |
| 28. #13095496 | C8 | semidirect |
| 30. D8×C97 | C8 | semidirect |
| 40. #11715906 | D8 | direct (N × H) |
| 41. D4×C97 | C2×C8 | semidirect |
| 43. D388 | C2×C8 | semidirect |
| 46. C8×C97 | C2×C8 | semidirect |
| 47. #11715895 | C2×C8 | semidirect |
| 65. C97 | C8×D8 | semidirect |
| 85. D8 | #11715906 | direct (N × H) |
| 99. D4 | C2×#11715906 | semidirect |
| 112. C8 | C2×#11715906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#11715906 | 2 |
| #20261825 | 2 |
| D4⋊#11715906 | 2 |
| C8×#11715906 | 2 |
| D8×#87604 | 2 |
| C8×D8 | 97 |