Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
248 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 126 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 | semidirect |
| 17. #13095519 | C8 | semidirect |
| 41. #11715897 | C2×C8 | semidirect |
| 57. D97 | #322 | semidirect |
| 59. C97 | C2×#322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095519 | 2 |
| #20261577 | 2 |
| C4×C8×D97 | 2 |
| C2×#322 | 97 |