Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
438 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 115 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×D4×Dic157 | C2 | semidirect |
| 2. C2×#19097692 | C2 | semidirect |
| 3. C2×#19097692 | C2 | semidirect |
| 4. #23757176 | C2 | semidirect |
| 5. #23757036 | C2 | semidirect |
| 6. #23757027 | C2 | semidirect |
| 24. C2×D8×C157 | C4 | semidirect |
| 56. C2×D4×C157 | C2×C4 | semidirect |
| 63. C2×C8×C157 | C2×C4 | semidirect |
| 76. C2×Dic157 | D8 | semidirect |
| 100. D4×C157 | C22⋊C4 | semidirect |
| 146. C157 | #1879 | semidirect |
| 160. C2×D8 | Dic157 | semidirect |
| 184. C2×D4 | C2×Dic157 | semidirect |
| 201. C2×C8 | C2×Dic157 | semidirect |
| 233. D4 | C22⋊Dic157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic157 | 2 |
| C2×#19097692 | 2 |
| #23757176 | 2 |
| #23757036 | 2 |
| #23757027 | 2 |
| C22×D8×C157 | 2 |
| #1879 | 157 |