Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 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. #20261471 | C2 | semidirect |
| 2. #20261446 | C2 | semidirect |
| 3. #20261088 | C2 | semidirect |
| 4. #20261037 | C2 | semidirect |
| 5. #20261027 | C2 | semidirect |
| 6. #20260949 | C2 | semidirect |
| 8. C8×Dic194 | C2 | semidirect |
| 9. C4×#13095500 | C2 | semidirect |
| 10. #20260815 | C2 | semidirect |
| 11. #486×C97 | C2 | semidirect |
| 123. C97 | #3361 | semidirect |
| 127. #486 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261471 | 2 |
| #20261446 | 2 |
| #20261088 | 2 |
| #20261037 | 2 |
| #20261027 | 2 |
| #20260949 | 2 |
| #20260927 | 2 |
| C8×Dic194 | 2 |
| C4×#13095500 | 2 |
| #20260815 | 2 |
| #486×C97 | 2 |
| #3361 | 97 |