Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. C2×#15690745 | C2 | semidirect |
| 3. #20260745 | C2 | semidirect |
| 5. C2×#15690728 | C2 | semidirect |
| 6. #20260693 | C2 | semidirect |
| 12. C2×#13095499 | C4 | semidirect |
| 107. C97 | #1977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095499 | 2 |
| C2×#15690745 | 2 |
| #20260745 | 2 |
| #20260740 | 2 |
| C2×#15690728 | 2 |
| #20260693 | 2 |
| C2×#100×C97 | 2 |
| #1977 | 97 |