Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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. #20261471 | C2 | semidirect |
| 2. #20261442 | C2 | semidirect |
| 3. #20261088 | C2 | semidirect |
| 4. #20261081 | C2 | semidirect |
| 5. #20261033 | C2 | semidirect |
| 6. #20261031 | C2 | semidirect |
| 7. #20260948 | C2 | semidirect |
| 8. #20260859 | C2 | semidirect |
| 9. C4×#13095499 | C2 | semidirect |
| 10. D8×Dic97 | C2 | semidirect |
| 123. C97 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261471 | 2 |
| #20261442 | 2 |
| #20261088 | 2 |
| #20261081 | 2 |
| #20261033 | 2 |
| #20261031 | 2 |
| #20260948 | 2 |
| #20260859 | 2 |
| C4×#13095499 | 2 |
| D8×Dic97 | 2 |
| #459×C97 | 2 |
| #3361 | 97 |