Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
528 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 206 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 |
|---|---|---|
| 2. #20261601 | C2 | semidirect |
| 6. C2×#13095519 | C4 | semidirect |
| 17. C2×#11715897 | C2×C4 | semidirect |
| 23. C2×C4×D97 | C8 | semidirect |
| 44. C2×C4×C97 | C2×C8 | semidirect |
| 47. C2×Dic97 | C2×C8 | semidirect |
| 76. D97 | #336 | semidirect |
| 78. C97 | C2×#336 | semidirect |
| 132. C2×C4 | #13095519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095519 | 2 |
| #20261601 | 2 |
| C2×C42×D97 | 2 |
| C2×#336 | 97 |