Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
144 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20260565 | C2 | semidirect |
| 4. #20260564 | C2 | semidirect |
| 5. #368×C97 | C2 | semidirect |
| 52. D97 | #368 | direct (N × H) |
| 54. C97 | C2×#368 | semidirect |
| 59. #368 | D97 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D97 | 2 |
| #108×D97 | 2 |
| #20260565 | 2 |
| #20260564 | 2 |
| #368×C97 | 2 |
| C2×#368 | 97 |