Finite Group DatabasebetaFinite Group DatabasebetaOrder 38656.
316 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C151 | #2067 |
| commutator, Frattini, cosocle | C22×C8 | C23×C151 |
| prime radical | C22×D8×C151 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C151 ◁ C22×C4×C151 ◁ #405×C151 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2161×C151 | C2 | semidirect |
| 2. #2153×C151 | C2 | semidirect |
| 6. #1953×C151 | C2 | semidirect |
| 7. #1385×C151 | C2 | semidirect |
| 130. #13472 | C151 | direct (N × H) |
| 131. C151 | #13472 | direct (N × H) |
| 132. #2161 | C2×C151 | semidirect |
| 133. #2153 | C2×C151 | semidirect |
| 137. #1953 | C2×C151 | semidirect |
| 138. #1385 | C2×C151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2161×C151 | 2 |
| #2153×C151 | 2 |
| C2×#361×C151 | 2 |
| #1978×C151 | 2 |
| #1953×C151 | 2 |
| #1385×C151 | 2 |
| #13472 | 151 |