Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
426 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 426 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. #20261405 | C2 | semidirect |
| 2. #20261400 | C2 | semidirect |
| 3. #20261080 | C2 | semidirect |
| 4. #20261013 | C2 | semidirect |
| 5. #20261012 | C2 | semidirect |
| 6. #20260929 | C2 | semidirect |
| 7. #20260927 | C2 | semidirect |
| 8. C8×Dic194 | C2 | semidirect |
| 9. C4×D776 | C2 | semidirect |
| 10. #20260815 | C2 | semidirect |
| 11. #486×C97 | C2 | semidirect |
| 97. D388 | #41 | semidirect |
| 102. Dic194 | D8 | semidirect |
| 132. C97 | #3358 | semidirect |
| 136. #486 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261405 | 2 |
| #20261400 | 2 |
| #20261080 | 2 |
| #20261013 | 2 |
| #20261012 | 2 |
| #20260929 | 2 |
| #20260927 | 2 |
| C8×Dic194 | 2 |
| C4×D776 | 2 |
| #20260815 | 2 |
| #486×C97 | 2 |
| #3358 | 97 |