Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1072 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 287 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. C23×#11715906 | C2 | semidirect |
| 2. C2×C22⋊#11715906 | C2 | direct (N × H) |
| 5. C22×#11715906 | C22 | semidirect |
| 6. C22⋊#11715906 | C22 | direct (N × H) |
| 14. C2×#11715906 | C23 | semidirect |
| 26. C23×D97 | C8 | semidirect |
| 27. C23×D97 | C8 | semidirect |
| 30. C24×C97 | C8 | semidirect |
| 33. C23×C97 | C2×C8 | semidirect |
| 40. C22×D97 | C2×C8 | semidirect |
| 41. C22×D97 | C2×C8 | semidirect |
| 55. C22×C97 | C22⋊C8 | semidirect |
| 57. C22×C97 | C22×C8 | semidirect |
| 62. C2×D97 | C22⋊C8 | semidirect |
| 65. C2×D97 | C22×C8 | semidirect |
| 72. C2×C97 | C2×C22⋊C8 | semidirect |
| 75. D97 | C2×C22⋊C8 | semidirect |
| 79. C97 | C22×C22⋊C8 | semidirect |
| 98. C24 | #11715906 | semidirect |
| 123. C23 | C2×#11715906 | semidirect |
| 144. C22 | C22⋊#11715906 | direct (N × H) |
| 146. C22 | C22×#11715906 | semidirect |
| 155. C2 | C2×C22⋊#11715906 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11715906 | 2 |
| C2×C22⋊#11715906 | 2 |
| C24×#87604 | 2 |
| C22×C22⋊C8 | 97 |