Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
510 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 93 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. C22×D1336 | C2 | semidirect |
| 2. C22×#14581935 | C2 | semidirect |
| 3. C2×#19128828 | C2 | semidirect |
| 4. C2×#19128752 | C2 | semidirect |
| 5. #24923170 | C2 | semidirect |
| 6. #24923023 | C2 | semidirect |
| 7. C2×#102×C167 | C2 | semidirect |
| 40. C2×D668 | D4 | semidirect |
| 49. C2×C167⋊C8 | D4 | semidirect |
| 64. C2×C8×C167 | D4 | semidirect |
| 88. C2×Dic167 | D8 | semidirect |
| 143. C167 | #2011 | semidirect |
| 149. C2×#102 | D167 | semidirect |
| 205. C2×C8 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1336 | 2 |
| C22×#14581935 | 2 |
| C2×#19128828 | 2 |
| C2×#19128752 | 2 |
| #24923170 | 2 |
| #24923023 | 2 |
| C2×#102×C167 | 2 |
| #2011 | 167 |