Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1206 conjugacy classes of subgroups; only the 302 normal subgroups are shown.
This group has 1206 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 | C25×C83 | C23 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C83×#1444 | C2 | semidirect |
| 3. C83×#1443 | C2 | semidirect |
| 141. #17229 | C83 | direct (N × H) |
| 149. #1444 | C2×C83 | semidirect |
| 150. #1443 | C2×C83 | semidirect |
| 153. C83 | #17229 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#397×C83 | 2 |
| C83×#1444 | 2 |
| C83×#1443 | 2 |
| C83×#1440 | 2 |
| C83×#1439 | 2 |
| #17229 | 83 |