Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 2. #24909200 | C2 | semidirect |
| 3. #24909168 | C2 | semidirect |
| 4. C2×#19127486 | C2 | semidirect |
| 5. #24907506 | C2 | semidirect |
| 6. #24905560 | C2 | semidirect |
| 7. C83×#2155 | C2 | semidirect |
| 177. #2155 | D83 | semidirect |
| 183. C83 | #13401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917184 | 2 |
| #24909200 | 2 |
| #24909168 | 2 |
| C2×#19127486 | 2 |
| #24907506 | 2 |
| #24905560 | 2 |
| C83×#2155 | 2 |
| #13401 | 83 |