Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
1160 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 360 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 | C24 |
| commutator | C22 | C23×C4×C83 |
| Frattini, cosocle | C23 | C24×C83 |
| prime radical | C23×D4×C83 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C22⋊C4×C83 | C2 | semidirect |
| 3. #386×C83 | C2 | semidirect |
| 4. #381×C83 | C2 | semidirect |
| 5. #379×C83 | C2 | semidirect |
| 9. C22×D4×C83 | C4 | semidirect |
| 12. C23×C4×C83 | C22 | semidirect |
| 15. C2×C22⋊C4×C83 | C22 | semidirect |
| 16. C2×C22⋊C4×C83 | C22 | semidirect |
| 17. #95×C83 | C22 | semidirect |
| 22. C24×C83 | C2×C4 | semidirect |
| 30. C2×D4×C83 | C2×C4 | semidirect |
| 34. C22×C4×C83 | C2×C4 | semidirect |
| 49. C23×C83 | C22⋊C4 | semidirect |
| 87. #2308 | C83 | direct (N × H) |
| 88. C83 | #2308 | direct (N × H) |
| 90. C22×C22⋊C4 | C2×C83 | semidirect |
| 91. #386 | C2×C83 | semidirect |
| 92. #381 | C2×C83 | semidirect |
| 93. #379 | C2×C83 | semidirect |
| 97. C22×D4 | C4×C83 | semidirect |
| 100. C23×C4 | C22×C83 | semidirect |
| 103. C2×C22⋊C4 | C22×C83 | semidirect |
| 104. C2×C22⋊C4 | C22×C83 | semidirect |
| 105. #95 | C22×C83 | semidirect |
| 110. C24 | C2×C4×C83 | semidirect |
| 118. C2×D4 | C2×C4×C83 | semidirect |
| 122. C22×C4 | C2×C4×C83 | semidirect |
| 137. C23 | C22⋊C4×C83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D4×C83 | 2 |
| C22×C22⋊C4×C83 | 2 |
| #386×C83 | 2 |
| #381×C83 | 2 |
| #379×C83 | 2 |
| #2308 | 83 |