Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
456 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. C2×#19128070 | C2 | semidirect |
| 4. #24906181 | C2 | semidirect |
| 6. #24905818 | C2 | semidirect |
| 7. C83×#1302 | C2 | semidirect |
| 175. #1302 | D83 | semidirect |
| 176. C83 | #10134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918655 | 2 |
| #24918593 | 2 |
| C2×#19128070 | 2 |
| #24906181 | 2 |
| #24906073 | 2 |
| #24905818 | 2 |
| C83×#1302 | 2 |
| #10134 | 83 |