Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
444 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 105 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×#19127523 | C2 | semidirect |
| 3. C2×#19127514 | C2 | semidirect |
| 4. C2×#19127510 | C2 | semidirect |
| 5. C2×#19127479 | C2 | semidirect |
| 6. #24908356 | C2 | semidirect |
| 7. C83×#1972 | C2 | semidirect |
| 11. C2×#14581736 | C4 | semidirect |
| 12. C2×#14581733 | C4 | semidirect |
| 83. C83⋊C16 | C22⋊C4 | semidirect |
| 179. #1972 | D83 | semidirect |
| 180. C83 | #13249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128137 | 2 |
| C2×#19127523 | 2 |
| C2×#19127514 | 2 |
| C2×#19127510 | 2 |
| C2×#19127479 | 2 |
| #24908356 | 2 |
| C83×#1972 | 2 |
| #13249 | 83 |