Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 131 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. #24918028 | C2 | semidirect |
| 2. #24909626 | C2 | semidirect |
| 3. #24909618 | C2 | semidirect |
| 4. #24909557 | C2 | semidirect |
| 5. #24909554 | C2 | semidirect |
| 6. #24909524 | C2 | semidirect |
| 7. #24909516 | C2 | semidirect |
| 8. C2×Dic83⋊C16 | C2 | semidirect |
| 156. C83 | #33816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918028 | 2 |
| #24909626 | 2 |
| #24909618 | 2 |
| #24909557 | 2 |
| #24909554 | 2 |
| #24909524 | 2 |
| #24909516 | 2 |
| C2×Dic83⋊C16 | 2 |
| C83×#2215 | 2 |
| #33816 | 83 |