Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
404 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 128 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. #20261603 | C2 | semidirect |
| 6. #15690889 | C4 | semidirect |
| 10. C2×C4×#87604 | C4 | semidirect |
| 12. C2×#13095495 | C4 | semidirect |
| 16. C2×C8×D97 | C4 | semidirect |
| 17. C2×M16×C97 | C4 | semidirect |
| 24. C4×#87604 | C2×C4 | semidirect |
| 37. C2×#11715895 | C2×C4 | semidirect |
| 42. C2×C8×C97 | C2×C4 | semidirect |
| 93. D97 | H(3,ℤ/4) | semidirect |
| 95. C97 | C2×H(3,ℤ/4) | semidirect |
| 104. C2×M16 | #87604 | semidirect |
| 131. C2×C8 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690889 | 2 |
| #20261603 | 2 |
| C2×M16×D97 | 2 |
| C2×H(3,ℤ/4) | 97 |