Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
266 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 81 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. C4×#14581934 | C2 | semidirect |
| 3. #24922999 | C2 | semidirect |
| 4. #24922996 | C2 | semidirect |
| 5. #423×C167 | C2 | semidirect |
| 54. Dic334 | M16 | semidirect |
| 56. D668 | M16 | semidirect |
| 102. C167 | #1489 | semidirect |
| 105. #423 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14581950 | 2 |
| C4×#14581934 | 2 |
| #24922999 | 2 |
| #24922996 | 2 |
| #423×C167 | 2 |
| #1489 | 167 |