Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20261459 | C2 | semidirect |
| 2. #20261446 | C2 | semidirect |
| 3. #20261091 | C2 | semidirect |
| 4. #20261044 | C2 | semidirect |
| 5. #20261022 | C2 | semidirect |
| 7. #20260937 | C2 | semidirect |
| 8. C8×Dic194 | C2 | semidirect |
| 9. #20260820 | C2 | semidirect |
| 11. #487×C97 | C2 | semidirect |
| 121. C97 | #3360 | semidirect |
| 125. #487 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261459 | 2 |
| #20261446 | 2 |
| #20261091 | 2 |
| #20261044 | 2 |
| #20261022 | 2 |
| #20260953 | 2 |
| #20260937 | 2 |
| C8×Dic194 | 2 |
| #20260820 | 2 |
| C4×D776 | 2 |
| #487×C97 | 2 |
| #3360 | 97 |