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 |
|---|---|---|
| 5. #15690885 | C4 | semidirect |
| 8. #15690881 | C4 | semidirect |
| 59. C97 | #1389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261791 | 2 |
| D97⋊#108 | 2 |
| #20260770 | 2 |
| #1389 | 97 |