Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
316 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 61 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. #24909660 | C2 | semidirect |
| 3. #24908952 | C2 | semidirect |
| 4. #24905476 | C2 | semidirect |
| 6. #24905402 | C2 | semidirect |
| 160. C83 | #12290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918809 | 2 |
| #24909660 | 2 |
| #24908952 | 2 |
| #24905476 | 2 |
| #24905472 | 2 |
| #24905402 | 2 |
| C83×#2232 | 2 |
| #12290 | 83 |