Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
274 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×#15690744 | C2 | semidirect |
| 2. C2×#15690742 | C2 | semidirect |
| 6. #20260601 | C2 | semidirect |
| 7. #336×C97 | C2 | semidirect |
| 100. C97 | #2092 | semidirect |
| 107. #336 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690744 | 2 |
| C2×#15690742 | 2 |
| C2×#15690732 | 2 |
| #20260637 | 2 |
| #20260601 | 2 |
| #336×C97 | 2 |
| #2092 | 97 |