Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
200 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20261825 | C2 | direct (N × H) |
| 24. C2×#11715895 | C8 | semidirect |
| 25. C8×D97 | C8 | semidirect |
| 27. C2×C8×C97 | C8 | semidirect |
| 44. C8×C97 | C2×C8 | semidirect |
| 45. #11715895 | C2×C8 | semidirect |
| 60. C2×C97 | #335 | semidirect |
| 62. D97 | #335 | semidirect |
| 66. C97 | C2×#335 | semidirect |
| 89. C2×C8 | #11715906 | semidirect |
| 111. C8 | C2×#11715906 | semidirect |
| 129. C2 | #20261825 | 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 |
| #20261825 | 2 |
| C2×C8×#87604 | 2 |
| C2×#335 | 97 |