Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
596 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 216 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, Frattini, cosocle | C23 | C24×C83 |
| prime radical | C2×#121×C83 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C4⋊C4×C83 | C2 | semidirect |
| 3. #397×C83 | C2 | semidirect |
| 4. #390×C83 | C2 | semidirect |
| 5. #386×C83 | C2 | semidirect |
| 6. #382×C83 | C2 | semidirect |
| 7. C4×C22⋊C4×C83 | C2 | semidirect |
| 92. #2504 | C83 | direct (N × H) |
| 93. C83 | #2504 | direct (N × H) |
| 95. C22×C4⋊C4 | C2×C83 | semidirect |
| 96. #397 | C2×C83 | semidirect |
| 97. #390 | C2×C83 | semidirect |
| 98. #386 | C2×C83 | semidirect |
| 99. #382 | C2×C83 | semidirect |
| 100. C4×C22⋊C4 | C2×C83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#121×C83 | 2 |
| C22×C4⋊C4×C83 | 2 |
| #397×C83 | 2 |
| #390×C83 | 2 |
| #386×C83 | 2 |
| #382×C83 | 2 |
| C4×C22⋊C4×C83 | 2 |
| #2504 | 83 |