Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
312 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. C2×#15690733 | C2 | semidirect |
| 4. C2×#15690728 | C2 | semidirect |
| 5. #20260504 | C2 | semidirect |
| 6. #20260499 | C2 | semidirect |
| 10. #15690840 | C4 | semidirect |
| 117. C97 | #1908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690840 | 2 |
| C2×#15690817 | 2 |
| C2×#15690733 | 2 |
| C2×#15690728 | 2 |
| #20260504 | 2 |
| #20260499 | 2 |
| #417×C97 | 2 |
| #1908 | 97 |