Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
264 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. #20260761 | C2 | semidirect |
| 3. #20260732 | C2 | semidirect |
| 4. #20260709 | C2 | semidirect |
| 5. #20260708 | C2 | semidirect |
| 6. #20260491 | C2 | semidirect |
| 7. #416×C97 | C2 | semidirect |
| 119. C97 | #2053 | semidirect |
| 123. #416 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261533 | 2 |
| #20260761 | 2 |
| #20260732 | 2 |
| #20260709 | 2 |
| #20260708 | 2 |
| #20260491 | 2 |
| #416×C97 | 2 |
| #2053 | 97 |