Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
272 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 122 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×#13095514 | C2 | semidirect |
| 2. C22⋊#13095514 | C2 | direct (N × H) |
| 5. C2×#13095514 | C22 | semidirect |
| 29. C23×C97 | C16 | semidirect |
| 49. C22×C97 | C2×C16 | semidirect |
| 57. C2×C97 | C22⋊C16 | semidirect |
| 62. C97 | C2×C22⋊C16 | semidirect |
| 91. C23 | #13095514 | semidirect |
| 111. C22 | C2×#13095514 | semidirect |
| 119. C2 | C22⋊#13095514 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095514 | 2 |
| C22⋊#13095514 | 2 |
| C23×#11715895 | 2 |
| C2×C22⋊C16 | 97 |