Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
284 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 104 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 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C83 |
| prime radical | C22×D4×C83 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ C2×C42×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#107×C83 | C2 | semidirect |
| 2. C2×C4⋊C8×C83 | C2 | semidirect |
| 6. #389×C83 | C2 | semidirect |
| 7. #340×C83 | C2 | semidirect |
| 119. #2067 | C83 | direct (N × H) |
| 120. C83 | #2067 | direct (N × H) |
| 121. C2×#107 | C2×C83 | semidirect |
| 122. C2×C4⋊C8 | C2×C83 | semidirect |
| 126. #389 | C2×C83 | semidirect |
| 127. #340 | C2×C83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#107×C83 | 2 |
| C2×C4⋊C8×C83 | 2 |
| C2×#102×C83 | 2 |
| #390×C83 | 2 |
| #389×C83 | 2 |
| #340×C83 | 2 |
| #2067 | 83 |