Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
248 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 3. #20261577 | C2 | direct (N × H) |
| 17. C2×#11715897 | C8 | semidirect |
| 43. #11715897 | C2×C8 | semidirect |
| 57. C2×C97 | #322 | semidirect |
| 62. C97 | C2×#322 | semidirect |
| 119. C2 | #20261577 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11715897 | 2 |
| #20261577 | 2 |
| C2×C8×Dic97 | 2 |
| C2×#322 | 97 |