Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1072 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 338 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. C23×#11715897 | C2 | semidirect |
| 2. C2×#15690867 | C2 | direct (N × H) |
| 5. C22×#11715897 | C22 | semidirect |
| 6. #15690867 | C22 | direct (N × H) |
| 14. C2×#11715897 | C23 | semidirect |
| 17. C23×D97 | C8 | semidirect |
| 36. C22×D97 | C2×C8 | semidirect |
| 47. C22×C97 | C22⋊C8 | semidirect |
| 55. C2×D97 | C22×C8 | semidirect |
| 59. C2×C97 | C2×C22⋊C8 | semidirect |
| 65. C97 | C22×C22⋊C8 | semidirect |
| 116. C22 | #15690867 | direct (N × H) |
| 125. C2 | C2×#15690867 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11715897 | 2 |
| C2×#15690867 | 2 |
| C23×C4×D97 | 2 |
| C22×C22⋊C8 | 97 |