Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
260 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 108 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 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C4×C83 |
| Frattini, cosocle | C42 | C23×C83 |
| prime radical | #532×C83 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #423×C83 | C2 | semidirect |
| 3. C2×C4⋊C8×C83 | C2 | semidirect |
| 4. #332×C83 | C2 | semidirect |
| 5. #331×C83 | C2 | semidirect |
| 90. #1547 | C83 | direct (N × H) |
| 91. C83 | #1547 | direct (N × H) |
| 93. #423 | C2×C83 | semidirect |
| 94. C2×C4⋊C8 | C2×C83 | semidirect |
| 95. #332 | C2×C83 | semidirect |
| 96. #331 | C2×C83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #532×C83 | 2 |
| #423×C83 | 2 |
| C2×C4⋊C8×C83 | 2 |
| #332×C83 | 2 |
| #331×C83 | 2 |
| #1547 | 83 |