Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
324 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. #24909736 | C2 | semidirect |
| 2. #24909600 | C2 | semidirect |
| 3. #24906852 | C2 | semidirect |
| 4. #24905518 | C2 | semidirect |
| 5. #24905424 | C2 | semidirect |
| 6. D4⋊(C83⋊C16) | C2 | semidirect |
| 141. C83 | #12392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909736 | 2 |
| #24909600 | 2 |
| #24906852 | 2 |
| #24905518 | 2 |
| #24905424 | 2 |
| D4⋊(C83⋊C16) | 2 |
| C83×#3334 | 2 |
| #12392 | 83 |