Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. #20261288 | C2 | semidirect |
| 3. #20261102 | C2 | semidirect |
| 4. #20261098 | C2 | semidirect |
| 5. #20261096 | C2 | semidirect |
| 6. #20261093 | C2 | semidirect |
| 7. #20260732 | C2 | semidirect |
| 8. #20260731 | C2 | semidirect |
| 9. #20260729 | C2 | semidirect |
| 10. C2×#15690720 | C2 | semidirect |
| 11. #416×C97 | C2 | semidirect |
| 126. C97 | #3135 | semidirect |
| 136. #416 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261288 | 2 |
| #20261281 | 2 |
| #20261102 | 2 |
| #20261098 | 2 |
| #20261096 | 2 |
| #20261093 | 2 |
| #20260732 | 2 |
| #20260731 | 2 |
| #20260729 | 2 |
| C2×#15690720 | 2 |
| #416×C97 | 2 |
| #3135 | 97 |