Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
168 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 74 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. #20261662 | C2 | direct (N × H) |
| 8. C2×#13095486 | C4 | semidirect |
| 9. C16×D97 | C4 | semidirect |
| 11. C2×C16×C97 | C4 | semidirect |
| 21. #13095486 | C2×C4 | semidirect |
| 23. C16×C97 | C2×C4 | semidirect |
| 46. C2×C97 | #367 | semidirect |
| 48. D97 | #367 | semidirect |
| 51. C97 | C2×#367 | semidirect |
| 60. C2×C16 | #87604 | semidirect |
| 74. C16 | C2×#87604 | semidirect |
| 99. C2 | #20261662 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690879 | 2 |
| #20261662 | 2 |
| C2×C16×D97 | 2 |
| C2×#367 | 97 |