Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
706 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | #386 |
| commutator | C22×C4 | C22×C4×C83 |
| Frattini, cosocle | C2×C42 | C23×C83 |
| prime radical | C83×#2541 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C83×#2975 | C2 | semidirect |
| 3. C83×#1800 | C2 | semidirect |
| 4. C83×#1545 | C2 | semidirect |
| 5. C83×#1303 | C2 | semidirect |
| 42. C4⋊C8×C83 | D4 | semidirect |
| 145. #9405 | C83 | direct (N × H) |
| 153. #2975 | C2×C83 | semidirect |
| 155. #1800 | C2×C83 | semidirect |
| 156. #1545 | C2×C83 | semidirect |
| 157. #1303 | C2×C83 | semidirect |
| 158. C83 | #9405 | direct (N × H) |
| 195. C4⋊C8 | D4×C83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C83×#2975 | 2 |
| C83×#2541 | 2 |
| C83×#1800 | 2 |
| C83×#1545 | 2 |
| C83×#1303 | 2 |
| #9405 | 83 |