Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. C4×#13095495 | C2 | semidirect |
| 4. #20260503 | C2 | semidirect |
| 5. C4×M16×C97 | C2 | semidirect |
| 15. #15690726 | C4 | direct (N × H) |
| 32. #13095495 | C2×C4 | semidirect |
| 42. M16×C97 | C2×C4 | semidirect |
| 85. C4×C97 | #100 | semidirect |
| 96. C97 | C4×#100 | semidirect |
| 100. C4×M16 | D97 | semidirect |
| 133. M16 | C4×D97 | semidirect |
| 182. C4 | #15690726 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D388 | 2 |
| C2×#15690726 | 2 |
| C4×#13095495 | 2 |
| #20260503 | 2 |
| C4×M16×C97 | 2 |
| C4×#100 | 97 |