Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
196 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 3. #20261622 | C2 | semidirect |
| 4. C16×#87604 | C2 | semidirect |
| 8. #15690885 | C4 | semidirect |
| 9. #15690884 | C4 | semidirect |
| 16. #15690750 | C4 | semidirect |
| 17. #15690749 | C4 | semidirect |
| 19. M32×C97 | C4 | semidirect |
| 28. #13095514 | C2×C4 | semidirect |
| 35. #13095486 | C2×C4 | semidirect |
| 37. C16×C97 | C2×C4 | semidirect |
| 59. #87604 | M32 | direct (N × H) |
| 69. C97 | C4×M32 | semidirect |
| 82. M32 | #87604 | direct (N × H) |
| 106. C16 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261791 | 2 |
| C2×C8×#87604 | 2 |
| #20261622 | 2 |
| C16×#87604 | 2 |
| M32×D97 | 2 |
| C4×M32 | 97 |