Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #20260743 | C2 | semidirect |
| 5. C2×#15690728 | C2 | semidirect |
| 6. #20260493 | C2 | semidirect |
| 7. #344×C97 | C2 | semidirect |
| 12. C2×Dic388 | C4 | semidirect |
| 13. C2×#13095500 | C4 | semidirect |
| 108. C97 | #1902 | semidirect |
| 114. #344 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690843 | 2 |
| #20261501 | 2 |
| #20260753 | 2 |
| #20260743 | 2 |
| C2×#15690728 | 2 |
| #20260493 | 2 |
| #344×C97 | 2 |
| #1902 | 97 |