Finite Group DatabasebetaFinite Group DatabasebetaOrder 38656.
402 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 90 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 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C151 |
| prime radical | #3213×C151 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1967×C151 | C2 | semidirect |
| 3. #1569×C151 | C2 | semidirect |
| 4. #1557×C151 | C2 | semidirect |
| 5. #1527×C151 | C2 | semidirect |
| 6. #1525×C151 | C2 | semidirect |
| 7. #1291×C151 | C2 | semidirect |
| 188. #10496 | C151 | direct (N × H) |
| 189. C151 | #10496 | direct (N × H) |
| 191. #1967 | C2×C151 | semidirect |
| 192. #1569 | C2×C151 | semidirect |
| 193. #1557 | C2×C151 | semidirect |
| 194. #1527 | C2×C151 | semidirect |
| 195. #1525 | C2×C151 | semidirect |
| 196. #1291 | C2×C151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3213×C151 | 2 |
| #1967×C151 | 2 |
| #1569×C151 | 2 |
| #1557×C151 | 2 |
| #1527×C151 | 2 |
| #1525×C151 | 2 |
| #1291×C151 | 2 |
| #10496 | 151 |