Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23757645 | C2 | semidirect |
| 2. #23757553 | C2 | semidirect |
| 3. D4×#11929434 | C2 | semidirect |
| 4. #23757023 | C2 | semidirect |
| 5. #23757018 | C2 | semidirect |
| 6. #23757017 | C2 | semidirect |
| 49. #11929434 | D8 | semidirect |
| 58. D4×C157 | SD16 | semidirect |
| 85. C157 | #1665 | semidirect |
| 139. D4 | #14578942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757645 | 2 |
| #23757553 | 2 |
| D4×#11929434 | 2 |
| #23757023 | 2 |
| #23757018 | 2 |
| #23757017 | 2 |
| #459×C157 | 2 |
| #1665 | 157 |