Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
958 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 238 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, Frattini, cosocle | C42 | C24×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. C2×#491×C83 | C2 | semidirect |
| 3. C2×#489×C83 | C2 | semidirect |
| 4. C83×#1662 | C2 | direct (N × H) |
| 5. C2×#330×C83 | C2 | semidirect |
| 6. C2×#329×C83 | C2 | semidirect |
| 17. #491×C83 | C22 | semidirect |
| 19. #489×C83 | C22 | semidirect |
| 25. #330×C83 | C22 | semidirect |
| 26. #329×C83 | C22 | semidirect |
| 144. C2×#1662 | C83 | direct (N × H) |
| 146. C2×C83 | #1662 | direct (N × H) |
| 150. C2×#491 | C2×C83 | semidirect |
| 151. C2×#489 | C2×C83 | semidirect |
| 152. #1662 | C2×C83 | direct (N × H) |
| 153. C2×#330 | C2×C83 | semidirect |
| 154. C2×#329 | C2×C83 | semidirect |
| 155. C83 | C2×#1662 | direct (N × H) |
| 166. #491 | C22×C83 | semidirect |
| 168. #489 | C22×C83 | semidirect |
| 174. #330 | C22×C83 | semidirect |
| 175. #329 | C22×C83 | semidirect |
| 294. C2 | C83×#1662 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#562×C83 | 2 |
| C2×#491×C83 | 2 |
| C2×#489×C83 | 2 |
| C83×#1662 | 2 |
| C2×#330×C83 | 2 |
| C2×#329×C83 | 2 |
| C2×#1662 | 83 |