Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
354 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 2. #20261445 | C2 | semidirect |
| 3. #20261138 | C2 | semidirect |
| 4. #20261074 | C2 | semidirect |
| 5. #20261050 | C2 | semidirect |
| 6. #20261026 | C2 | semidirect |
| 7. #20260984 | C2 | semidirect |
| 8. C4×#13095498 | C2 | semidirect |
| 9. #20260812 | C2 | semidirect |
| 10. #20260776 | C2 | semidirect |
| 11. #477×C97 | C2 | semidirect |
| 122. C97 | #3357 | semidirect |
| 128. #477 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261451 | 2 |
| #20261445 | 2 |
| #20261138 | 2 |
| #20261074 | 2 |
| #20261050 | 2 |
| #20261026 | 2 |
| #20260984 | 2 |
| C4×#13095498 | 2 |
| #20260812 | 2 |
| #20260776 | 2 |
| #477×C97 | 2 |
| #3357 | 97 |