Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
138 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 47 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. #24923670 | C2 | semidirect |
| 3. #24923073 | C2 | semidirect |
| 6. C16×Dic167 | C2 | semidirect |
| 7. #358×C167 | C2 | semidirect |
| 66. C167 | #2242 | semidirect |
| 71. #358 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923670 | 2 |
| #24923654 | 2 |
| #24923073 | 2 |
| #24923071 | 2 |
| #24923069 | 2 |
| C16×Dic167 | 2 |
| #358×C167 | 2 |
| #2242 | 167 |