Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
276 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 82 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. #20261754 | C2 | semidirect |
| 2. C4×#13095519 | C2 | semidirect |
| 3. Q8⋊#11715897 | C2 | semidirect |
| 4. #20261583 | C2 | semidirect |
| 27. #13095512 | C8 | semidirect |
| 54. Q8×C97 | C2×C8 | semidirect |
| 66. D388 | C2×C8 | semidirect |
| 99. C97 | #1476 | semidirect |
| 153. Q8 | #13095519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261754 | 2 |
| C4×#13095519 | 2 |
| Q8⋊#11715897 | 2 |
| #20261583 | 2 |
| C4×#13095512 | 2 |
| #1476 | 97 |