Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 69 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. #24923326 | C2 | semidirect |
| 3. #24923010 | C2 | semidirect |
| 4. #24923008 | C2 | semidirect |
| 5. C4×M16×C167 | C2 | semidirect |
| 90. C167 | #1529 | semidirect |
| 94. C4×M16 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923803 | 2 |
| #24923326 | 2 |
| #24923010 | 2 |
| #24923008 | 2 |
| C4×M16×C167 | 2 |
| #1529 | 167 |