Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1008 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 285 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. C22×#13095495 | C2 | semidirect |
| 3. #20260698 | C2 | direct (N × H) |
| 4. C2×#15690722 | C2 | semidirect |
| 5. C22×M16×C97 | C2 | semidirect |
| 15. C2×#13095495 | C22 | semidirect |
| 16. C22×#11715895 | C22 | semidirect |
| 17. #15690722 | C22 | semidirect |
| 20. C2×M16×C97 | C22 | semidirect |
| 21. C22×C8×C97 | C22 | semidirect |
| 40. C2×#11715895 | C23 | semidirect |
| 50. C2×C8×C97 | C23 | semidirect |
| 60. C22×D97 | M16 | semidirect |
| 90. C2×D97 | C2×M16 | semidirect |
| 97. C2×C97 | #407 | semidirect |
| 102. C97 | C2×#407 | semidirect |
| 105. C22×M16 | D97 | semidirect |
| 120. C2×M16 | C2×D97 | semidirect |
| 122. C22×C8 | C2×D97 | semidirect |
| 152. C2×C8 | C22×D97 | semidirect |
| 200. C2 | #20260698 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D97 | 2 |
| C22×#13095495 | 2 |
| #20260698 | 2 |
| C2×#15690722 | 2 |
| C22×M16×C97 | 2 |
| C2×#407 | 97 |