Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
5150 conjugacy classes of subgroups; only the 939 normal subgroups are shown.
This group has 5150 conjugacy classes of subgroups — too many to draw. Only its 939 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C22×D83 |
| commutator, cosocle | C23×C83 | C25 |
| Frattini | C23 | C24×D83 |
| Fitting | C2×#376×C83 | C2 |
| socle | C24×C83 | C24 |
| hypercenter | C2×#376 | D83 |
| hypocenter | C83 | C2×#2397 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23×C4 ◁ C2×#376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C4×D332 | C2 | semidirect |
| 2. #24910744 | C2 | direct (N × H) |
| 3. C2×#19127638 | C2 | semidirect |
| 4. C2×#19127611 | C2 | semidirect |
| 5. C2×#376×C83 | C2 | semidirect |
| 9. C2×C4×D332 | C22 | semidirect |
| 12. #19127638 | C22 | semidirect |
| 13. #19127611 | C22 | semidirect |
| 15. #376×C83 | C22 | semidirect |
| 31. C2×C42×C83 | D4 | semidirect |
| 53. C42×C83 | C2×D4 | semidirect |
| 84. C2×C83 | #2397 | semidirect |
| 92. C2×#376 | D83 | semidirect |
| 93. C83 | C2×#2397 | semidirect |
| 103. #376 | C2×D83 | semidirect |
| 119. C2×C42 | D332 | semidirect |
| 141. C42 | C2×D332 | semidirect |
| 172. C2 | #24910744 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D332 | 2 |
| #24910744 | 2 |
| C2×#19127638 | 2 |
| C2×#19127611 | 2 |
| C2×#376×C83 | 2 |
| C2×#2397 | 83 |