Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
344 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 73 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. #24909692 | C2 | semidirect |
| 3. #24909612 | C2 | semidirect |
| 4. #24905511 | C2 | semidirect |
| 5. #24905426 | C2 | semidirect |
| 140. C83 | #12374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic332 | 2 |
| #24909692 | 2 |
| #24909612 | 2 |
| #24905511 | 2 |
| #24905426 | 2 |
| D4⋊(C83⋊C16) | 2 |
| C83×#1675 | 2 |
| #12374 | 83 |