Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
756 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 249 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. #20261502 | C2 | semidirect |
| 3. #20260717 | C2 | semidirect |
| 4. C2×#15690726 | C2 | semidirect |
| 5. #568×C97 | C2 | semidirect |
| 13. C2×#13095495 | C22 | semidirect |
| 14. #15690728 | C22 | semidirect |
| 15. #15690726 | C22 | semidirect |
| 18. C2×M16×C97 | C22 | semidirect |
| 77. C97 | #2888 | semidirect |
| 80. #568 | D97 | semidirect |
| 93. C2×M16 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690856 | 2 |
| #20261502 | 2 |
| #20260717 | 2 |
| C2×#15690726 | 2 |
| #568×C97 | 2 |
| #2888 | 97 |