Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
848 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#19127500 | C2 | semidirect |
| 3. C2×#19127497 | C2 | semidirect |
| 4. #24907866 | C2 | semidirect |
| 5. C83×#1886 | C2 | semidirect |
| 8. #19128417 | C4 | semidirect |
| 174. #1886 | D83 | semidirect |
| 175. C83 | #12776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128417 | 2 |
| C2×#19127500 | 2 |
| C2×#19127497 | 2 |
| #24907866 | 2 |
| C83×#1886 | 2 |
| #12776 | 83 |