Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
284 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #20260753 | C2 | semidirect |
| 3. #20260708 | C2 | semidirect |
| 4. #20260690 | C2 | semidirect |
| 5. #427×C97 | C2 | semidirect |
| 11. C2×Dic388 | C4 | semidirect |
| 12. C2×#13095500 | C4 | semidirect |
| 13. C2×D776 | C4 | semidirect |
| 97. C97 | #1976 | semidirect |
| 99. #427 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690832 | 2 |
| #20260753 | 2 |
| #20260708 | 2 |
| #20260690 | 2 |
| #427×C97 | 2 |
| #1976 | 97 |