Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 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. #20261782 | C2 | semidirect |
| 2. #20261776 | C2 | semidirect |
| 3. #20261659 | C2 | semidirect |
| 4. #20261653 | C2 | semidirect |
| 5. #20261651 | C2 | semidirect |
| 6. #20261625 | C2 | semidirect |
| 18. #15690755 | C4 | semidirect |
| 19. #15690754 | C4 | semidirect |
| 20. #15690751 | C4 | semidirect |
| 22. D16×C97 | C4 | semidirect |
| 34. Dic388 | C2×C4 | semidirect |
| 39. #13095486 | C2×C4 | semidirect |
| 41. D8×C97 | C2×C4 | semidirect |
| 42. C16×C97 | C2×C4 | semidirect |
| 76. C97 | AGL(1,ℤ/16) | semidirect |
| 91. D16 | #87604 | semidirect |
| 107. D8 | C2×#87604 | semidirect |
| 118. C16 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261782 | 2 |
| #20261776 | 2 |
| #20261659 | 2 |
| #20261653 | 2 |
| #20261651 | 2 |
| #20261625 | 2 |
| #20261169 | 2 |
| AGL(1,ℤ/16) | 97 |