Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
408 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 408 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×#19127525 | C2 | semidirect |
| 4. C2×#19127478 | C2 | semidirect |
| 6. #24908335 | C2 | semidirect |
| 7. C2×#362×C83 | C2 | semidirect |
| 11. C2×#14581738 | C4 | semidirect |
| 12. C2×#14581735 | C4 | semidirect |
| 167. C2×#362 | D83 | semidirect |
| 172. C83 | #13250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128142 | 2 |
| C2×#19127525 | 2 |
| C2×#19127512 | 2 |
| C2×#19127478 | 2 |
| #24908354 | 2 |
| #24908335 | 2 |
| C2×#362×C83 | 2 |
| #13250 | 83 |