Finite Group DatabasebetaFinite Group DatabasebetaOrder 38656.
830 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 238 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C151 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C151 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1663×C151 | C2 | direct (N × H) |
| 129. C2×C151 | #1663 | direct (N × H) |
| 132. C2×#1663 | C151 | direct (N × H) |
| 133. C151 | C2×#1663 | direct (N × H) |
| 137. #1663 | C2×C151 | direct (N × H) |
| 262. C2 | #1663×C151 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#564×C151 | 2 |
| C2×#501×C151 | 2 |
| C2×#491×C151 | 2 |
| #1663×C151 | 2 |
| C2×#330×C151 | 2 |
| C2×#1663 | 151 |