Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
690 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2973 | C2 | semidirect |
| 3. C83×#1555 | C2 | semidirect |
| 4. C83×#1466 | C2 | semidirect |
| 5. C83×#1285 | C2 | semidirect |
| 49. C4⋊C8×C83 | D4 | semidirect |
| 178. #9457 | C83 | direct (N × H) |
| 187. #2973 | C2×C83 | semidirect |
| 189. #1555 | C2×C83 | semidirect |
| 190. #1466 | C2×C83 | semidirect |
| 191. #1285 | C2×C83 | semidirect |
| 192. C83 | #9457 | direct (N × H) |
| 236. 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×#2973 | 2 |
| C83×#2541 | 2 |
| C83×#1555 | 2 |
| C83×#1466 | 2 |
| C83×#1285 | 2 |
| #9457 | 83 |