Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. C2×C4⋊#11929434 | C2 | semidirect |
| 3. #23757139 | C2 | semidirect |
| 4. #23757035 | C2 | semidirect |
| 15. C4×D4×C157 | C4 | semidirect |
| 94. C157 | #1804 | semidirect |
| 105. C4×D4 | Dic157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11929434 | 2 |
| C2×#19097692 | 2 |
| #23757139 | 2 |
| #23757035 | 2 |
| C2×C4×D4×C157 | 2 |
| #1804 | 157 |