Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
396 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 1. C2×C4⋊#11715897 | C2 | semidirect |
| 2. C2×#15690867 | C2 | semidirect |
| 3. C2×C4×#11715897 | C2 | semidirect |
| 21. C2×#11715897 | D4 | semidirect |
| 25. C2×D388 | C8 | semidirect |
| 72. C4×C97 | C22⋊C8 | semidirect |
| 84. C97 | #1954 | semidirect |
| 160. C4 | #15690867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11715897 | 2 |
| C2×#15690867 | 2 |
| C2×C4×#11715897 | 2 |
| C2×#15690772 | 2 |
| #1954 | 97 |