Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#19127517 | C2 | semidirect |
| 5. #24908212 | C2 | semidirect |
| 6. #24905544 | C2 | semidirect |
| 7. C83×#2141 | C2 | semidirect |
| 163. #2141 | D83 | semidirect |
| 167. C83 | #13414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128086 | 2 |
| C2×#19127517 | 2 |
| C2×#19127515 | 2 |
| #24909178 | 2 |
| #24908212 | 2 |
| #24905544 | 2 |
| C83×#2141 | 2 |
| #13414 | 83 |