Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
162 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 61 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×#15690907 | C2 | semidirect |
| 2. C4⋊#13095523 | C2 | semidirect |
| 3. #20261832 | C2 | semidirect |
| 4. C4×#13095523 | C2 | semidirect |
| 17. #13095523 | D4 | semidirect |
| 45. C4×C97 | M32 | semidirect |
| 54. C97 | #2169 | semidirect |
| 102. C4 | #15690907 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690907 | 2 |
| C4⋊#13095523 | 2 |
| #20261832 | 2 |
| C4×#13095523 | 2 |
| #20261763 | 2 |
| #2169 | 97 |