Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
330 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 87 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. #24909719 | C2 | semidirect |
| 2. #24909715 | C2 | semidirect |
| 4. #24907070 | C2 | semidirect |
| 5. #24907068 | C2 | semidirect |
| 6. C16×C83⋊C8 | C2 | semidirect |
| 7. C83×#2248 | C2 | semidirect |
| 100. #2248 | D83 | semidirect |
| 106. C83 | #12518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909719 | 2 |
| #24909715 | 2 |
| #24909712 | 2 |
| #24907070 | 2 |
| #24907068 | 2 |
| C16×C83⋊C8 | 2 |
| C83×#2248 | 2 |
| #12518 | 83 |