Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
140 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 7. #15690750 | C4 | semidirect |
| 13. M32×C97 | C4 | semidirect |
| 58. C97 | #1377 | semidirect |
| 68. M32 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690750 | 2 |
| C2×#15690720 | 2 |
| C2×M32×C97 | 2 |
| #1377 | 97 |