Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
168 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20260513 | C2 | semidirect |
| 4. #20260512 | C2 | semidirect |
| 5. #347×C97 | C2 | semidirect |
| 10. #15690749 | C4 | semidirect |
| 11. C16×D97 | C4 | semidirect |
| 27. #13095486 | C2×C4 | semidirect |
| 31. C16×C97 | C2×C4 | semidirect |
| 59. D97 | #347 | direct (N × H) |
| 61. C97 | C2×#347 | semidirect |
| 66. #347 | D97 | direct (N × H) |
| 92. C16 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M32×D97 | 2 |
| #97×D97 | 2 |
| #20260513 | 2 |
| #20260512 | 2 |
| #347×C97 | 2 |
| C2×#347 | 97 |