Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
432 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 97 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. #24909252 | C2 | semidirect |
| 2. C2×#19127511 | C2 | semidirect |
| 3. #24909175 | C2 | semidirect |
| 4. C2×#19127483 | C2 | semidirect |
| 5. #24907496 | C2 | semidirect |
| 6. #24905568 | C2 | semidirect |
| 35. #14581732 | D4 | semidirect |
| 215. C83 | #13386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909252 | 2 |
| C2×#19127511 | 2 |
| #24909175 | 2 |
| C2×#19127483 | 2 |
| #24907496 | 2 |
| #24905568 | 2 |
| C83×#3054 | 2 |
| #13386 | 83 |