Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
140 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 54 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. #15690884 | C4 | semidirect |
| 12. #15690750 | C4 | semidirect |
| 15. M32×C97 | C4 | semidirect |
| 60. C97 | #1377 | semidirect |
| 71. M32 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261791 | 2 |
| C2×#15690864 | 2 |
| M32×D97 | 2 |
| #1377 | 97 |