Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
248 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20261819 | C2 | direct (N × H) |
| 15. #13095519 | C8 | semidirect |
| 17. C2×#11715897 | C8 | semidirect |
| 22. C2×#11715895 | C8 | semidirect |
| 23. C8×D97 | C8 | semidirect |
| 25. C2×C8×C97 | C8 | semidirect |
| 37. #11715897 | C2×C8 | semidirect |
| 38. C8×C97 | C2×C8 | semidirect |
| 39. #11715895 | C2×C8 | semidirect |
| 50. C2×C97 | #322 | semidirect |
| 52. D97 | #322 | semidirect |
| 55. C97 | C2×#322 | semidirect |
| 77. C2×C8 | #11715906 | semidirect |
| 94. C8 | C2×#11715906 | semidirect |
| 107. C2 | #20261819 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11715906 | 2 |
| #20261819 | 2 |
| C2×C8×#87604 | 2 |
| C2×#322 | 97 |