Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
256 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 11. C4⋊#11715895 | C4 | semidirect |
| 70. C4×C97 | #107 | semidirect |
| 84. C97 | #1947 | semidirect |
| 155. C4 | #15690743 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690743 | 2 |
| C2×C4⋊#11715895 | 2 |
| #20260605 | 2 |
| #20260497 | 2 |
| C4×C4⋊C4×C97 | 2 |
| #1947 | 97 |