Finite Group DatabasebetaFinite Group DatabasebetaOrder 38656.
176 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 74 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×C151 | C2×D16 |
| commutator, Frattini, cosocle | C2×C16 | C23×C151 |
| prime radical | C23×C151 | D16 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C22×C8×C151 ◁ C22×C16×C151 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #1424×C151 | C2 | semidirect |
| 4. #1416×C151 | C2 | semidirect |
| 72. #13714 | C151 | direct (N × H) |
| 73. C151 | #13714 | direct (N × H) |
| 76. #1424 | C2×C151 | semidirect |
| 77. #1416 | C2×C151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2216×C151 | 2 |
| C2×#366×C151 | 2 |
| #1424×C151 | 2 |
| #1416×C151 | 2 |
| C22⋊C32×C151 | 2 |
| #13714 | 151 |