Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
392 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20261465 | C2 | semidirect |
| 3. #20261080 | C2 | semidirect |
| 4. #20261023 | C2 | semidirect |
| 5. #20261022 | C2 | semidirect |
| 6. #20260934 | C2 | semidirect |
| 7. #20260932 | C2 | semidirect |
| 8. C8×Dic194 | C2 | semidirect |
| 9. #20260826 | C2 | semidirect |
| 10. C4×#13095500 | C2 | semidirect |
| 11. #486×C97 | C2 | semidirect |
| 98. Dic194 | SD16 | semidirect |
| 99. Dic194 | #41 | semidirect |
| 126. C97 | #3362 | semidirect |
| 130. #486 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261465 | 2 |
| #20261405 | 2 |
| #20261080 | 2 |
| #20261023 | 2 |
| #20261022 | 2 |
| #20260934 | 2 |
| #20260932 | 2 |
| C8×Dic194 | 2 |
| #20260826 | 2 |
| C4×#13095500 | 2 |
| #486×C97 | 2 |
| #3362 | 97 |