Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
232 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 232 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. #20260477 | C2 | semidirect |
| 4. #20260476 | C2 | semidirect |
| 5. #330×C97 | C2 | semidirect |
| 56. D97 | #330 | direct (N × H) |
| 58. C97 | C2×#330 | semidirect |
| 63. #330 | D97 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #125×D97 | 2 |
| #97×D97 | 2 |
| #20260477 | 2 |
| #20260476 | 2 |
| #330×C97 | 2 |
| C2×#330 | 97 |