Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
272 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 84 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. C22×#13095525 | C2 | semidirect |
| 2. C22⋊#13095525 | C2 | direct (N × H) |
| 5. C2×#13095525 | C22 | semidirect |
| 27. C23×C97 | C16 | semidirect |
| 30. C22×D97 | C16 | semidirect |
| 31. C22×D97 | C16 | semidirect |
| 48. C22×C97 | C2×C16 | semidirect |
| 55. C2×D97 | C2×C16 | semidirect |
| 63. C2×C97 | C22⋊C16 | semidirect |
| 66. D97 | C22⋊C16 | semidirect |
| 70. C97 | C2×C22⋊C16 | semidirect |
| 103. C23 | #13095525 | semidirect |
| 127. C22 | C2×#13095525 | semidirect |
| 137. C2 | C22⋊#13095525 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095525 | 2 |
| C22⋊#13095525 | 2 |
| C23×#11715906 | 2 |
| C2×C22⋊C16 | 97 |