Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
280 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 83 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. #24909738 | C2 | semidirect |
| 2. #24909690 | C2 | semidirect |
| 4. #24907057 | C2 | semidirect |
| 6. #24905379 | C2 | semidirect |
| 68. C16×C83 | SD16 | semidirect |
| 111. C83 | #12508 | semidirect |
| 172. C16 | #13050578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909738 | 2 |
| #24909690 | 2 |
| #24909686 | 2 |
| #24907057 | 2 |
| #24907052 | 2 |
| #24905379 | 2 |
| C83×#2248 | 2 |
| #12508 | 83 |