Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
174 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 50 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. D8×#87604 | C2 | semidirect |
| 2. #20261661 | C2 | semidirect |
| 3. #20261647 | C2 | semidirect |
| 4. C16×#87604 | C2 | semidirect |
| 12. D1552 | C4 | semidirect |
| 13. #15690751 | C4 | semidirect |
| 15. D16×C97 | C4 | semidirect |
| 23. D776 | C2×C4 | semidirect |
| 26. #13095486 | C2×C4 | semidirect |
| 27. D8×C97 | C2×C4 | semidirect |
| 28. C16×C97 | C2×C4 | semidirect |
| 48. #87604 | D16 | direct (N × H) |
| 57. C97 | C4×D16 | semidirect |
| 67. D16 | #87604 | direct (N × H) |
| 77. D8 | C2×#87604 | semidirect |
| 85. C16 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×#87604 | 2 |
| #20261661 | 2 |
| #20261647 | 2 |
| C16×#87604 | 2 |
| D16×D97 | 2 |
| C4×D16 | 97 |