Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
340 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 165 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. #24923678 | C2 | semidirect |
| 3. #24923674 | C2 | semidirect |
| 4. #24923671 | C2 | semidirect |
| 40. M16×C167 | Q8 | semidirect |
| 41. C2×C8×C167 | Q8 | semidirect |
| 80. C167 | #3164 | semidirect |
| 112. M16 | Dic334 | semidirect |
| 113. C2×C8 | Dic334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923897 | 2 |
| #24923678 | 2 |
| #24923674 | 2 |
| #24923671 | 2 |
| #24923311 | 2 |
| #24923307 | 2 |
| C2×#19128766 | 2 |
| #405×C167 | 2 |
| #3164 | 167 |