Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. #24923677 | C2 | semidirect |
| 4. #24923676 | C2 | semidirect |
| 5. #24923670 | C2 | semidirect |
| 6. #24923669 | C2 | semidirect |
| 48. #14581934 | Q8 | semidirect |
| 72. M16×C167 | Q8 | semidirect |
| 124. C167 | #3166 | semidirect |
| 176. M16 | Dic334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923822 | 2 |
| C2×#19128823 | 2 |
| #24923677 | 2 |
| #24923676 | 2 |
| #24923670 | 2 |
| #24923669 | 2 |
| #24923312 | 2 |
| #24923311 | 2 |
| #24923309 | 2 |
| M16×Dic167 | 2 |
| #428×C167 | 2 |
| #3166 | 167 |