Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
562 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#19128017 | C2 | semidirect |
| 2. C2×#19128012 | C2 | semidirect |
| 3. #24907541 | C2 | semidirect |
| 4. #24905823 | C2 | semidirect |
| 5. #24905823 | C2 | semidirect |
| 6. #24905350 | C2 | semidirect |
| 210. C83 | #9992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128017 | 2 |
| C2×#19128012 | 2 |
| #24907541 | 2 |
| #24905823 | 2 |
| #24905350 | 2 |
| C83×#3192 | 2 |
| #9992 | 83 |