Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1008 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 242 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. C22×#13095521 | C2 | semidirect |
| 2. #20261706 | C2 | direct (N × H) |
| 3. C2×#15690867 | C2 | semidirect |
| 4. C2×C22⋊#11715897 | C2 | semidirect |
| 7. C2×#13095521 | C22 | semidirect |
| 8. C22×#11715897 | C22 | semidirect |
| 9. #15690867 | C22 | semidirect |
| 10. C22⋊#11715897 | C22 | semidirect |
| 23. C2×#11715897 | C23 | semidirect |
| 54. C23×C97 | M16 | semidirect |
| 66. C22×D97 | M16 | semidirect |
| 94. C22×C97 | C2×M16 | semidirect |
| 104. C2×D97 | C2×M16 | semidirect |
| 111. C2×C97 | #407 | semidirect |
| 118. C97 | C2×#407 | semidirect |
| 184. C23 | #13095521 | semidirect |
| 221. C22 | C2×#13095521 | semidirect |
| 231. C2 | #20261706 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095521 | 2 |
| #20261706 | 2 |
| C2×#15690867 | 2 |
| C2×C22⋊#11715897 | 2 |
| C23×C4×D97 | 2 |
| C2×#407 | 97 |