Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1426 conjugacy classes of subgroups; only the 302 normal subgroups are shown.
This group has 1426 conjugacy classes of subgroups — too many to draw. Only its 302 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C83 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C83 |
| prime radical | C23×D4×C83 | C22 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C83×#1442 | C2 | semidirect |
| 2. C83×#1439 | C2 | semidirect |
| 3. C83×#1439 | C2 | semidirect |
| 160. #17271 | C83 | direct (N × H) |
| 167. #1442 | C2×C83 | semidirect |
| 168. #1439 | C2×C83 | semidirect |
| 169. #1439 | C2×C83 | semidirect |
| 172. C83 | #17271 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C83×#1442 | 2 |
| C83×#1439 | 2 |
| C83×#1438 | 2 |
| #17271 | 83 |