Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
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⋊#11929441 | C4 | direct (N × H) |
| 25. C4×Dic157 | C8 | semidirect |
| 32. C42×C157 | C8 | semidirect |
| 65. C4×C157 | C4×C8 | semidirect |
| 66. C4×C157 | C4⋊C8 | semidirect |
| 69. Dic157 | C4⋊C8 | semidirect |
| 79. C157 | C4×C4⋊C8 | semidirect |
| 112. C42 | #11929441 | semidirect |
| 150. C4 | C4×#11929441 | semidirect |
| 151. C4 | C4⋊#11929441 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11929441 | 2 |
| C2×C4×#11929441 | 2 |
| #23758139 | 2 |
| C42×Dic157 | 2 |
| C4×C4⋊C8 | 157 |