Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
378 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 91 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. #24909184 | C2 | semidirect |
| 4. #24908378 | C2 | semidirect |
| 6. #24905578 | C2 | semidirect |
| 7. C83×#2153 | C2 | semidirect |
| 164. #2153 | D83 | semidirect |
| 170. C83 | #13443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128144 | 2 |
| #24909213 | 2 |
| #24909184 | 2 |
| #24908378 | 2 |
| #24908361 | 2 |
| #24905578 | 2 |
| C83×#2153 | 2 |
| #13443 | 83 |