Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
504 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 192 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 | C22×D4×C83 | C22 |
| 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. #398×C83 | C2 | semidirect |
| 3. #397×C83 | C2 | semidirect |
| 5. #389×C83 | C2 | semidirect |
| 6. #385×C83 | C2 | semidirect |
| 86. #2724 | C83 | direct (N × H) |
| 87. C83 | #2724 | direct (N × H) |
| 89. #398 | C2×C83 | semidirect |
| 90. #397 | C2×C83 | semidirect |
| 92. #389 | C2×C83 | semidirect |
| 93. #385 | C2×C83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#123×C83 | 2 |
| #398×C83 | 2 |
| #397×C83 | 2 |
| #390×C83 | 2 |
| #389×C83 | 2 |
| #385×C83 | 2 |
| #2724 | 83 |