Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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. C2×#15690751 | C2 | semidirect |
| 2. #20261112 | C2 | semidirect |
| 3. C4×#13095486 | C2 | semidirect |
| 4. #493×C97 | C2 | semidirect |
| 18. #13095486 | D4 | semidirect |
| 43. C4×C97 | D16 | semidirect |
| 51. C97 | #2246 | semidirect |
| 54. #493 | D97 | semidirect |
| 94. C4 | #15690751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690751 | 2 |
| #20261112 | 2 |
| C4×#13095486 | 2 |
| #493×C97 | 2 |
| #2246 | 97 |