Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20261105 | C2 | semidirect |
| 3. #20261097 | C2 | semidirect |
| 4. #20261092 | C2 | semidirect |
| 5. #20261087 | C2 | semidirect |
| 6. #20260743 | C2 | semidirect |
| 9. C2×#15690733 | C2 | semidirect |
| 10. #20260691 | C2 | semidirect |
| 11. #544×C97 | C2 | semidirect |
| 128. C97 | #3137 | semidirect |
| 129. #544 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261311 | 2 |
| #20261105 | 2 |
| #20261097 | 2 |
| #20261092 | 2 |
| #20261087 | 2 |
| #20260743 | 2 |
| #20260734 | 2 |
| #20260729 | 2 |
| C2×#15690733 | 2 |
| #20260691 | 2 |
| #544×C97 | 2 |
| #3137 | 97 |