Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
550 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 105 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. #24918588 | C2 | semidirect |
| 2. C2×#19127981 | C2 | semidirect |
| 3. #24906145 | C2 | semidirect |
| 4. #24905862 | C2 | semidirect |
| 5. #24905784 | C2 | semidirect |
| 6. #24905358 | C2 | semidirect |
| 216. C83 | #10188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918588 | 2 |
| C2×#19127981 | 2 |
| #24906145 | 2 |
| #24905862 | 2 |
| #24905784 | 2 |
| #24905358 | 2 |
| C83×#3036 | 2 |
| #10188 | 83 |