Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
256 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. C2×#19128768 | C2 | semidirect |
| 3. #24923083 | C2 | direct (N × H) |
| 4. C2×M32×C167 | C2 | semidirect |
| 14. #19128768 | C22 | semidirect |
| 17. M32×C167 | C22 | semidirect |
| 75. C2×C167 | #361 | semidirect |
| 78. C167 | C2×#361 | semidirect |
| 81. C2×M32 | D167 | semidirect |
| 94. M32 | C2×D167 | semidirect |
| 155. C2 | #24923083 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1336 | 2 |
| C2×#19128768 | 2 |
| #24923083 | 2 |
| C2×M32×C167 | 2 |
| C2×#361 | 167 |