Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1008 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 234 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×#13095520 | C2 | semidirect |
| 2. #20261707 | C2 | direct (N × H) |
| 3. C2×#15690867 | C2 | semidirect |
| 6. C2×#13095520 | C22 | semidirect |
| 7. C22×#11715897 | C22 | semidirect |
| 8. #15690867 | C22 | semidirect |
| 19. C2×#11715897 | C23 | semidirect |
| 49. C22×D97 | M16 | semidirect |
| 75. C2×D97 | C2×M16 | semidirect |
| 81. C2×C97 | #407 | semidirect |
| 86. C97 | C2×#407 | semidirect |
| 168. C2 | #20261707 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095520 | 2 |
| #20261707 | 2 |
| C2×#15690867 | 2 |
| C23×C4×D97 | 2 |
| C2×#407 | 97 |