Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
366 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C83 |
| prime radical | C83×#3273 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C42×C83 ◁ #436×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C83×#2243 | C2 | semidirect |
| 3. C83×#2224 | C2 | semidirect |
| 4. C83×#1695 | C2 | semidirect |
| 5. C83×#1360 | C2 | semidirect |
| 6. C83×#1333 | C2 | semidirect |
| 7. C83×#1330 | C2 | semidirect |
| 10. #500×C83 | C22 | semidirect |
| 20. C4⋊C16×C83 | C22 | semidirect |
| 24. #346×C83 | C22 | semidirect |
| 25. #334×C83 | C22 | semidirect |
| 158. #12376 | C83 | direct (N × H) |
| 166. #2243 | C2×C83 | semidirect |
| 167. #2224 | C2×C83 | semidirect |
| 168. #1695 | C2×C83 | semidirect |
| 169. #1360 | C2×C83 | semidirect |
| 170. #1333 | C2×C83 | semidirect |
| 171. #1330 | C2×C83 | semidirect |
| 172. C83 | #12376 | direct (N × H) |
| 175. #500 | C22×C83 | semidirect |
| 185. C4⋊C16 | C22×C83 | semidirect |
| 189. #346 | C22×C83 | semidirect |
| 190. #334 | C22×C83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C83×#3273 | 2 |
| C83×#2243 | 2 |
| C83×#2224 | 2 |
| C83×#1695 | 2 |
| C83×#1360 | 2 |
| C83×#1333 | 2 |
| C83×#1330 | 2 |
| #12376 | 83 |