Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
196 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 196 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. #20260510 | C2 | semidirect |
| 4. C4×#13095486 | C2 | semidirect |
| 5. C4×C16×C97 | C2 | semidirect |
| 9. #15690749 | C4 | direct (N × H) |
| 24. #13095486 | C2×C4 | semidirect |
| 28. C16×C97 | C2×C4 | semidirect |
| 44. C4×C97 | M32 | semidirect |
| 53. C97 | C4×M32 | semidirect |
| 58. C4×C16 | D97 | semidirect |
| 81. C16 | C4×D97 | semidirect |
| 99. C4 | #15690749 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690749 | 2 |
| C4×C8×D97 | 2 |
| #20260510 | 2 |
| C4×#13095486 | 2 |
| C4×C16×C97 | 2 |
| C4×M32 | 97 |