Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
572 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 288 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. #20261700 | C2 | semidirect |
| 3. C4×#13095521 | C2 | semidirect |
| 4. C4×#13095519 | C2 | semidirect |
| 6. #15690898 | C4 | direct (N × H) |
| 20. #13095521 | C2×C4 | semidirect |
| 21. #13095519 | C2×C4 | semidirect |
| 57. C4×C97 | #131 | semidirect |
| 59. Dic97 | #131 | semidirect |
| 66. C97 | C4×#131 | semidirect |
| 126. C4 | #15690898 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690898 | 2 |
| #20261700 | 2 |
| C4×#13095521 | 2 |
| C4×#13095519 | 2 |
| C4×#13095512 | 2 |
| C4×#131 | 97 |