Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
128 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 48 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. #15690881 | C4 | semidirect |
| 11. #15690750 | C4 | semidirect |
| 14. M32×C97 | C4 | semidirect |
| 57. C97 | #1389 | semidirect |
| 66. M32 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690881 | 2 |
| #20261745 | 2 |
| M32×D97 | 2 |
| #1389 | 97 |