Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
316 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 166 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 |
|---|---|---|
| 6. C4⋊#11715897 | C4 | direct (N × H) |
| 25. C4×Dic97 | C8 | semidirect |
| 32. C42×C97 | C8 | semidirect |
| 65. C4×C97 | C4×C8 | semidirect |
| 66. C4×C97 | C4⋊C8 | semidirect |
| 69. Dic97 | C4⋊C8 | semidirect |
| 80. C97 | C4×C4⋊C8 | semidirect |
| 112. C42 | #11715897 | semidirect |
| 150. C4 | C4×#11715897 | semidirect |
| 151. C4 | C4⋊#11715897 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11715897 | 2 |
| C2×C4×#11715897 | 2 |
| #20261601 | 2 |
| C42×Dic97 | 2 |
| C4×C4⋊C8 | 97 |