Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
572 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 151 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. #24918042 | C2 | semidirect |
| 2. #24909611 | C2 | semidirect |
| 3. #24909566 | C2 | semidirect |
| 4. #24909499 | C2 | semidirect |
| 5. C83×#2150 | C2 | semidirect |
| 110. #2150 | D83 | semidirect |
| 111. C83 | #33819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918042 | 2 |
| #24909611 | 2 |
| #24909566 | 2 |
| #24909499 | 2 |
| C83×#2150 | 2 |
| #33819 | 83 |