Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
816 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C83 | #120 |
| commutator | C42 | C22×C4×C83 |
| Frattini, cosocle | C2×C42 | C23×C83 |
| prime radical | C2×#562×C83 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ C2×C42×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C83×#1992 | C2 | semidirect |
| 3. C83×#1959 | C2 | semidirect |
| 4. C2×#330×C83 | C2 | semidirect |
| 5. C2×#329×C83 | C2 | semidirect |
| 8. #562×C83 | C4 | semidirect |
| 148. #8508 | C83 | direct (N × H) |
| 156. #1992 | C2×C83 | semidirect |
| 157. #1959 | C2×C83 | semidirect |
| 158. C2×#330 | C2×C83 | semidirect |
| 159. C2×#329 | C2×C83 | semidirect |
| 160. C83 | #8508 | direct (N × H) |
| 163. #562 | C4×C83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#562×C83 | 2 |
| C83×#1992 | 2 |
| C83×#1959 | 2 |
| C2×#330×C83 | 2 |
| C2×#329×C83 | 2 |
| #8508 | 83 |