Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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. Q32×D97 | C2 | semidirect |
| 3. Dic1552 | C2 | semidirect |
| 4. #20260575 | C2 | semidirect |
| 5. #20260573 | C2 | semidirect |
| 6. #20260568 | C2 | semidirect |
| 7. SD64×C97 | C2 | semidirect |
| 52. C97 | #2264 | semidirect |
| 58. SD64 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261164 | 2 |
| Q32×D97 | 2 |
| Dic1552 | 2 |
| #20260575 | 2 |
| #20260573 | 2 |
| #20260568 | 2 |
| SD64×C97 | 2 |
| #2264 | 97 |