Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
392 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20260500 | C2 | semidirect |
| 4. #20260499 | C2 | semidirect |
| 5. #341×C97 | C2 | semidirect |
| 80. D97 | #341 | direct (N × H) |
| 82. C97 | C2×#341 | semidirect |
| 87. #341 | D97 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D97 | 2 |
| C22×C8×D97 | 2 |
| #20260500 | 2 |
| #20260499 | 2 |
| #341×C97 | 2 |
| C2×#341 | 97 |