Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
| 3. #20261072 | C2 | semidirect |
| 4. #20261062 | C2 | semidirect |
| 5. #20261017 | C2 | semidirect |
| 6. #20261012 | C2 | semidirect |
| 7. #20260982 | C2 | semidirect |
| 8. C4×#13095500 | C2 | semidirect |
| 9. #20260814 | C2 | semidirect |
| 10. #20260776 | C2 | semidirect |
| 11. #500×C97 | C2 | semidirect |
| 98. C8×C97 | #41 | semidirect |
| 123. C97 | #3353 | semidirect |
| 126. #500 | D97 | semidirect |
| 222. C8 | #13095512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261459 | 2 |
| #20261388 | 2 |
| #20261072 | 2 |
| #20261062 | 2 |
| #20261017 | 2 |
| #20261012 | 2 |
| #20260982 | 2 |
| C4×#13095500 | 2 |
| #20260814 | 2 |
| #20260776 | 2 |
| #500×C97 | 2 |
| #3353 | 97 |