Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
500 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 191 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. #20261848 | C2 | semidirect |
| 3. C2×C22⋊#11715906 | C2 | semidirect |
| 5. C22×#11715906 | C22 | semidirect |
| 6. C4⋊#11715906 | C22 | semidirect |
| 8. C22⋊#11715906 | C22 | semidirect |
| 9. C4×#11715906 | C22 | semidirect |
| 30. C2×D388 | C8 | semidirect |
| 31. C2×C22⋊D97 | C8 | semidirect |
| 32. D4×D97 | C8 | semidirect |
| 35. C2×D4×C97 | C8 | semidirect |
| 36. C23×C97 | C2×C8 | semidirect |
| 39. C22×D97 | C2×C8 | semidirect |
| 40. C22×D97 | C2×C8 | semidirect |
| 53. D4×C97 | C2×C8 | semidirect |
| 54. C2×C4×C97 | C2×C8 | semidirect |
| 55. C22⋊D97 | C2×C8 | semidirect |
| 56. C2×Dic97 | C2×C8 | semidirect |
| 57. D388 | C2×C8 | semidirect |
| 58. C4×D97 | C2×C8 | semidirect |
| 86. C97 | #2972 | semidirect |
| 108. C2×D4 | #11715906 | semidirect |
| 128. C23 | C2×#11715906 | semidirect |
| 131. D4 | C2×#11715906 | semidirect |
| 144. C2×C4 | 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 |
| #20261848 | 2 |
| C2×C22⋊#11715906 | 2 |
| C2×D4×#87604 | 2 |
| #2972 | 97 |